In this work we focus on a mathematical model of anisotropic and heterogeneous diffusion of tumor cells, a set of time-evolution parabolic equations. The model includes chemotaxis and haptotaxis effects, that appear in other biophysical phenomena. We compute numerical solutions considering spatial discretization by centered finite differences and time integration through an explicit Euler method. The choice of time-explicit algorithms is due to their greater ease of implementation, and performance, on GPU devices, despite the limitations related to their reduced stability properties. The codes used in this work are designed using CUDA. The CUDA platform (Compute Unified Device Architecture NVIDIA 2007), was designed to support GPU execution of programs and focuses on data parallelism.