The failure of chemotherapeutic drugs in treatment of various cancers is attributed to the acquisition of drug resistance. However, the invasion mechanisms of drug-resistant cancer cells remains incompletely understood. Here we address this question from a biophysical perspective by mapping the phenotypic alterations in ovarian cancer cells (OCCs) resistant to cisplatin and paclitaxel. We show that cisplatin-resistant (CisR), paclitaxel-resistant (PacR) and dual drug-resistant (i.e., resistant to both drugs) OCCs are softer and more contractile than drug-sensitive cells. Protease inhibition suppresses invasion of CisR cells but not of PacR and dual cells, suggesting protease-dependent mode of invasion in CisR cells and protease-independent mode in PacR and dual cells. Despite these differences, actomyosin contractility, mediated by the RhoA-ROCK2-Myosin IIB signaling pathway regulates both modes of invasion. Myosin IIB modulates matrix metalloproteinase-9 (MMP-9) secretion in CisR cells and nuclear squeezing in PacR and dual cells, thereby highlighting its importance as a potential therapeutic target for treatment of drug-resistant ovarian cancer cells.