In this talk, I will present a mechanobiochemical model for 3D cell migration which couples the actomyosin dynamics described by a system of reaction-diffusion equations on evolving volumes and a force balance viscoelastic mechanical model for the cell displacements. The novelty is that the pressure and contractile forces are influenced by actin and myosin spatiotemporal dynamics. To analyse the model, we carry out linear stability analysis to determine key bifurcation parameters and find analytical solutions close to bifurcation points. To validate theoretical findings as well as study the longtime behaviour of the model system away from bifurcation points, we employ the evolving finite element method in multi-dimensions. Solutions predicted from linear stability theory are replicated in the early stages of cell movement. Subsequently, both simple and complex cell deformations such as expansions, protrusions, contractions and translations of the cell are observed. This theoretical and computational framework set premises for studying more complex and experimentally-driven reaction kinetics involving, actin, myosin and other molecular species coupled to mechanical properties that play an important role in cell movement and deformation. Cell movement is critical in multicellular organisms due to its role in embryogenesis, wound healing, immune response, cancer metastasis, tumour invasion, and other biomedical processes.