The crucial role of microtubules in the mitotic-related segregation of chromosomes makes them an excellent target for anticancer microtubule targeting drugs (MTDs) such as vinflunine (VFL), colchicine (COL), and docetaxel (DTX). MTDs affect mitosis by directly perturbing the structural organisation of microtubules. By a direct assessment of the biomechanical properties of prostate cancer DU145 cells exposed to different MTDs using atomic force microscopy, we show that cell stiffening is a response to the application of all the studied MTDs (VFL, COL, DTX). Changes in cellular rigidity are typically attributed to remodelling of the actin filaments in the cytoskeleton. Here, we demonstrate that cell stiffening can be driven by crosstalk between actin filaments and microtubules in MTD-treated cells. Our findings improve the interpretation of biomechanical data obtained for living cells in studies of various physiological and pathological processes.