We propose a mathematical formalism and method for simulating the effects of the mechanochemical environment on the differentiation path and fate of stem cells. We provide a numerical methodology used for the numerical approximation of solutions of partial differential equations, based on a finite element approach, to describe the time evolution and spatial distribution of chemical and mechanical signals. Further, all cells are considered as independent entities, which may migrate through the domain of computation and which are subject to differentiation, division, and evolution of geometry. The model is applied to the development of adipose and muscle tissue. The developed framework is generic and can be applied to other similar biological processes and medical applications.