We developed an original computational model for cell deformation and migration capable of accounting for the cell sensitivity to the environment and its appropriate adaptation. This cell model is ultimately intended to be used to address tissue morphogenesis. Hence it has been designed to comply with four requirements: (1) the cell should be able to probe and sense its environment and respond accordingly; (2) the model should be easy to parametrize to adapt to different cell types; (3) the model should be able to extend to 3D cases; (4) simulations should be fast enough to integrate many interacting cells. The simulations carried out focused on two aspects: first, the general behaviour of the cell on a homogeneous substrate, as observed experimentally, for model validation. This enabled us to decipher the mechanisms by which the cell can migrate, highlighting respective influences of the adhesions lifetimes and their sensitivity to traction; second, it predicts the sensitivity of the cell to an anisotropic patterned substrate, in agreement with recently published experiments. The results show that mechanosensors simulated by the model make it possible to reproduce such experiments in terms of migration bias generated by the substrate anisotropy. Here again, the model provides a biomechanical explanation of this phenomenon, depending on cell-matrix interactions and adhesion maturation rate.