In the summer of 1964 Finkel married Reb Leizer Yudel's granddaughter, Leah, his second cousin and the eldest daughter of Rabbi Binyomin Beinush Finkel, who was his father's first cousin. He and his wife had 11 children. He continued to learn with "chavrutas" at all hours, stopping at 2 a.m.; his wife would bring their children to visit him at the yeshiva so he wouldn't have to take the time to walk home. He also began delivering "shiurim" in the yeshiva, which was headed by his father-in-law after the death of Reb Leizer Yudel in 1965. Upon the death of his father-in-law on 13 February 1990, Finkel was named rosh yeshiva of the Mir together with Rabbi Refoel Shmuelevitz (son of former Mir rosh yeshiva Rabbi Chaim Leib Shmuelevitz). Finkel took on the financial responsibility for the yeshiva.