The aim of the thesis is to provide a mathematical model in the framework of nonlinear elasticity in order to study the active response of biological cells lying over a stretched substrate: in particular, it is shown by several experimental findings that cells tend to re-orient themselves reaching a well-defined orientation, suggesting the link between the possible minimization of the elastic energy and the active remodelling process. We investigate several cases in the static domain: isotropic circular and elliptic cell as an inclusion in isotropic substrate, then transversely isotropic cell in isotropic substrate. We then study how modern theories of biological remodelling apply to the transient domain case, underlying the active response of cells.