The aim of this article is to show how continuous mathematical models for tumor dynamics can be solved efficiently using commodity Graphics Processing Units (GPUs) found in personal and portable computers. The test set of equations models haptotaxis and heterogeneous anisotropic diffusion of the cancer cells population. The numerical solution is obtained by using a second order finite difference Euler scheme. It is proven that, as the space resolution improves, the GPU implementation of the numerical scheme shows an increasingly better performance than that of the Central Processing Units (CPUs)