We propose a model for mechanotransduction in biological cells. The model addresses the bidirectional coupling between signalling processes and cell mechanics and consists of bulk and surface reaction-diffusion equations for the biochemistry coupled to the equations of elasticity for the cellular mechanics. A numerical method based on bulk-surface finite elements is proposed for the approximation of the coupled system. Simulation results illustrating novel emergent features that arise on coupling mechanics and signalling will be presented. Time permitting, we will discuss the analysis of the model equations as well as the numerical analysis of the numerical methods. Extensions to other constitutive assumptions for the mechanics may also be discussed.