A common feature of cancer cells is the alteration of kinases and biochemical signalling pathways enabling transformed growth on soft matrices, whereas cytoskeletal protein alterations are thought to be a secondary issue. However, we report here that cancer cells from different tissues can be toggled between transformed and rigidity-dependent growth states by the absence or presence of mechanosensory modules, respectively. In various cancer lines from different tissues, cells had over tenfold fewer rigidity-sensing contractions compared with normal cells from the same tissues. Restoring normal levels of cytoskeletal proteins, including tropomyosins, restored rigidity sensing and rigidity-dependent growth. Further depletion of other rigidity sensor proteins, including myosin IIA, restored transformed growth and blocked sensing. In addition, restoration of rigidity sensing to cancer cells inhibited tumour formation and changed expression patterns. Thus, the depletion of rigidity-sensing modules through alterations in cytoskeletal protein levels enables cancer cell growth on soft surfaces, which is an enabling factor for cancer progression.