The activity of the proteasome, a polyfunctional enzymatic complex, is known to undergo changes during cancer development. This phenomenon is probably caused by the changes in subunit composition of proteasomes. In this work, we studied the chymotrypsin-like activity of proteasomes; their subunit composition; and their association in breast cancer, head and neck squamous cell carcinoma, endometrial cancer, renal cancer, bladder cancer, stomach cancer, and colorectal cancer. The increase in proteasome activity was revealed in most cancer tissues compared with adjacent tissues, except for the renal cell carcinoma. Changes in proteasome activity in cancer tissues compared with correspondent normal tissues observed in combination with an increased expression of immune subunits and/or proteasome activator PA28 associated with activity of 20S proteasome. In breast cancer, head and neck squamous cell carcinoma, bladder cancer, stomach cancer, and colorectal cancer, we additionally found the higher expression of Rpt6 subunit of the 19S-subunit in 26S proteasome. Correlations between chymotrypsin-like proteasome activity and subunit expressions were found in human cancer tissues. Thus, we suggest that proteasome activation and changes in its subunit composition play an important role in cancer pathogenesis.