Resistance to the chemotherapeutic agents in the clinical management of cancer remains a significant challenge, and the mechanical environment of cancer cells is one of the major determinants of this. Stiffening of the environment is usually associated with increased chemoresistance of cancer cells, although this process depends on the type of cancer. Breast cancer is the most frequently diagnosed cancer, and more than half a million people die from it each year worldwide. In this study, we used the most frequent (70% of diagnosed cases) breast cancer phenotype, representing the MCF-7 cell line, to investigate the influence of surface stiffness on its sensitivity to one of the most commonly used anticancer drugs—doxorubicin. We showed that the mechanical environment affected MCF-7 proliferation, adhesion, and the expression and activation of mitogen-activated protein kinases (MAPKs). Furthermore, the role of MAPKs in response to doxorubicin was dependent on surface stiffness; nevertheless, surface stiffness did not affect MCF-7 resistance to doxorubicin.