In this project, we deal with the numerical approximation of problems described by a phase field model, which is nowadays popular to describe substances sharing sharp interfaces. We present the basis of the theory of mixtures required to introduce the spinodal decomposition and state the Cahn-Hilliard equations. Then, we use a four species model for tumor growth phenomenon, based on the theory of mixtures. Using the finite element method, we characterize the time evolution of a tumor, as well as the concentration of nutrients, in a wide range of scenarios described by a set of parameters.