The recrystallization process in polycrystalline material was studied using the newly developed two-dimensional model based on the vertex concept. In the model presented below the microstructure of polycrystalline material is represented by two-dimensional network of grains. The initial microstructure is characterized by topology, crystal orientations and stored energy values of the grains. The boundary energies and mobilities are anisotropic in general. Additional driving forces in recrystallization, are exerted on vertices and are derived from the stored energy gradients between adjacent grains. The nucleation mechanism of a given type is selected at the start of the calculations. Two different nucleation types were tested. Deformation texture, stored energy distribution and initial microstructure are input parameters of the model. The goal of the calculations is the prediction of texture and microstructure modification during recrystallization. A comparison of predicted and experimental characteristics enables the verification of the model assumptions.