This talk presents a numerical study of a system of partial differential equations consisting of a parabolic, an elliptic, and a hyperbolic equation, that be used to describe cell migration in elastic tissues by integrating chemotaxis, interstitial fluid pressure, and tissue displacement. In this framework, the system couples a Keller–Segel-type model for cell density and chemical concentration with an elliptic equation for fluid pressure and a wave-type equation for tissue displacement. Cell transport is driven by a nonlinear convective velocity that depends on the chemoattractant gradient, Darcy flow induced by the pressure field, and the tissue displacement velocity, while chemoattractant transport is advected only by Darcy flow. We propose a semidiscrete finite difference method on nonuniform grids, which can be seen as a fully discrete-in-space piecewise linear finite element method. Using an appropriate discrete norm, we establish second-order spatial error estimates for all variables. Finally, we present numerical simulations illustrating the theoretical results and the interplay between chemotaxis and tissue mechanics.