Richard Raymond Shaw, son of Raymond Leo Shaw and Viola EHzabeth Karafiat, was born at St. Anthony's Hospital in Chicago, Illinois, on June 6, 1931, and baptized a month later at Saints Cyril and Methodius Church on South Hermitage Avenue. He grew up in Cicero, Illinois, where he attended St. Frances of Rome School until 1941 when his family moved to Elmwood Park, Illinois, and completed his elementary education at St. Vincent Ferrer School in River Forest. He graduated with honors from Fenwick High School in Oak Park, Illinois, in 1949, and then pursued college studies at DePaul University in Chicago. His close association with Dominican priests and brothers and Sinsinawa Dominican Sisters in River Forest and Oak Park encouraged him to enter the Dominican Novitiate at St. Peter Martyr Priory in Winona, Minnesota, where he was assigned Francis as a religious name and later made his first profession on August 31, 1952.

Philosophical studies followed at the Dominican House of Studies in River Forest, Illinois, until 1955 when Brother Francis was sent to the College of St. Albert in Oakland, California, to begin theological studies along with a number of student brothers from St. Albert's Province assigned to studies in Holy Name Province at a time when the studia in River Forest and Dubuque were seriously overcrowded. On June 14, 1956, he was ordained a deacon at St. Patrick 's Seminary Chapel in Menlo Park, California. In September 1956, the new Priory of St. Rose was formally opened in Dubuque, Iowa, and Francis with several of his confreres were called back by the Provincial, John Marr, to finish their theological courses in the Central Province studium. On May 24, 1958, Francis was ordained a priest in St. Rose Priory Chapel in Dubuque by the Most Reverend Edward Celestine Daly, O.P., Dominican Bishop of Des Moines, Iowa. On the following day, Pentecost Sunday, he celebrated his First Solemn Mass at his home parish of St. Vincent Ferrer in River Forest.

Father Shaw's first assignment was to Albuquerque, New Mexico, to the staff of Aquinas Newman Center and to the faculty of St. Joseph College on the Rio Grande (later renamed the University of Albuquerque; the school ceased operations in 1988). In the fall of 1959, he was sent to St. Pius V Priory in Chicago for a special assignment to teach at Saint Xavier College in Chicago and to help develop instructional materials for the theology and literature component of the Xavier Plan of Liberal Education, a collaborative project designed by Dominicans of the Albertus Magnus Lyceum and the Chicago Province of the Sisters of Mercy. In September of 1964, Father Shaw was assigned to serve as superior at the newly established St. Dominic's House (Euclid Avenue) on Chicago's South Side and was appointed associate professor of English and theology and chairman of the Theology Department at St. Xavier College. He also wrote a weekly column, "Here's the Answer," for The New World, Chicago's Archdiocesan newspaper.

At the end of the spring semester of 1967, he was approved to pursue doctoral studies in theology and literature at Fordham University in New York, but those plans were changed abruptly on May 12, 1967, when he was elected Prior of St. Thomas Priory in River Forest, Illinois, the Dominican community of Aquinas Institute of Philosophy. In addition to serving as Prior, Father Shaw continued conducting a liturgy seminar at St. Xavier College, teaching courses in liturgy and in literary theory at Aquinas institute, and offering introductory courses in liturgy and spirituality for the Alexian Brothers' novices and postulants at Alexian Brothers' Hospital in Chicago. The late 1960's presented special difficulties for anyone responsible for seminary training and religious formation. Father Shaw and the religious and academic administrators of the Province tried to meet these new challenges by establishing a formation team and by attempting to develop a more coordinated training program between the novitiate and houses of philosophy and theology that allowed more flexibility in accommodating canonical requirements with post-conciliar directives on religious life.

In the early fall of 1968, Father Shaw and the Dominican community at Aquinas Institute of Philosophy hosted the General Chapter of the Dominican Order that devoted two months of intense work to produce a complete revision of the Book of Constitutions and Ordinations for the Order based upon the norms of the Second Vatican Council. In late May of 1969, the River Forest community hosted the Eighth Provincial Chapter of St. Albert the Great Province that took six weeks to draw up all the particular legislation required by the Order's newly revised Constitutions. This Chapter named Father Shaw Director of the newly formed Provincial Formation Team.

In 1972, Aquinas Institute of Philosophy was merged with the faculty of Theology in Dubuque, Iowa. Father Shaw then joined the Provincial Staff as Secretary of the Province and moved to St. Albert the Great Provincial House located on Bennett Avenue in Chicago 's Jackson Highlands neighborhood. Then on November 20, 1973, he was elected Prior of St. Pius V Priory in Chicago. He continued as Prior until he was named Socius and Vicar Provincial in 1976. After completing his term in Provincial administration in 1983, Father Shaw took a semester of sabbatical studies at Aquinas Institute of Theology in St. Louis, Missouri, before returning to St. Pius V Priory in Chicago for a six-month project that produced a new translation of the Liber Constitutionum et Ordinationum for use in all the English-speaking Provinces and Vicariates of the Order.

In February 1985, Father Shaw joined the staff of the Metropolitan Tribunal of the Archdiocese of Chicago and also began part-time service in the Chancery Office of the Archdiocese. In December of 1986 he was named full-time Assistant Chancellor of the Archdiocese by Joseph Cardinal Bernardin. During this time, Father Shaw had been given permission by his Prior and his Provincial to care for his mother who was suffering a series of debilitating illnesses that led ultimately to her death on December 10, 1986. On October 19, 1987, Father Shaw moved to St. Vincent Ferrer Priory in River Forest where he could care for his mother's only sister, Mary Karafiat, who died on December 11, 1989. While concentrating his efforts on aiding her convalescence, Father Shaw developed a digestive disorder that medical tests revealed to be a rare type of malignant duodenal tumor. Surgery at Loyola Medical Center in Maywood, Illinois, proved ineffective since smaller cancerous growths not detected by earlier testing procedures were discovered scattered throughout his lower abdomen. Father Shaw continued to carry out his responsibilities to his family, his religious community, and the Archdiocese of Chicago for as long as he retained sufficient strength. Francis Shaw died peacefully at 12:25 p.m. on June 14, 1990, in Loyola Medical Center, Maywood, Illinois. Mass of the Resurrection was celebrated on June 18 at St. Vincent Ferrer Church in River Forest with Father Donald Goergen, Prior Provincial, presiding. Father Benjamin Russell preached the homily, and his Eminence, Joseph Cardinal Bernardin, Archbishop of Chicago, present in the sanctuary, led the final commendation. Most of the Vocals of the Thirteenth Provincial Chapter, which was taking place at the time of his death, were present to bid "Franny" a fond farewell. He was buried with his Dominican Brothers in the community plot at All Saints Cemetery in Des Plaines, Illinois.