Cell migration emerges in diverse biological processes, including wound healing, tissue invasion of tumor cells, and formation of neural crest and vasculature. The migration can be directed by various biophysical cues, such as chemotactic gradients, electric fields, substrate geometry, and substrate stiffness. Cell migration has been studied in various experimental conditions. However, due to experimental limitations, the mechanisms of cell migration are not fully understood. To overcome these limitations, we have developed a computational biomechanical model that tackles various phenomena related to mesenchymal cell migration on two-dimensional substrates, such as durotaxis, contact inhibition of locomotion, and contact guidance.