Rabbi Finkel acquired most of his Torah knowledge during his studies at the yeshiva.

In 1931, he studied under the Chofetz Chaim, and in 1933-34 under Rav Yitzchok Zev Soloveitchik, the Brisker Rov.

He married the daughter of Rav Shmuel Greineman, the Chazon Ish's brother-in-law.

Three other sons in-law act as associate Roshei Yeshiva, they are Rabbis Binyomin Carlebach, Nachman Levovitz, and Yisroel Glustein (who also has his own shiur in the Mir) .

Another of his sons-in law, Rabbi Ahron Lopiansky, is rosh yeshiva of Yeshiva of Greater Washington in Silver Spring, Maryland.