Konstantinopolsky played several times in Soviet Chess Championships. In 1931, he tied for 3rd-5th (7th URS-ch semifinal), in Moscow. In 1934, he tied for 11th-13th in Tbilisi (9th URS-ch sf). In April/May 1937, he tied for 2nd-3rd with Viacheslav Ragozin, behind Grigory Levenfish, in Tbilisi (10th URS-ch), with a score of 12/19. In 1938, he tied for 11th-12th in Kiev (URS-ch sf). In 1940, he tied for 4th-7th in Kiev (URS-ch sf), with a score of 9½/16. In September/October 1940, he tied for 13th-16th in Moscow (12th URS-ch), with a score of 8/19.