Cancer development is a complex and dynamic problem, which cannot be described without the aid of mathematical models. The paper reviews a multistage model aimed at solving biomechanical problems. In the multistage modelling of solid avascular tumors, stochastic methods as Monte Carlo are also utilized as well as taking into account the impact of chemical interactions on the growth and nutrition of the cancer site. These include the mutual impact of proteins, the p53 gene and the vascular endothelial growth factor. Recently discovered molecular processes in the cells could be directly integrated into the model. This model could be used for numerical analysis of real tumor evolution with different initial and boundary conditions. Since the model involves the processes of gene regulation, it can be applied to the study of the effects of laser thermal therapy based on the protein-protein interactions, directly targeting the affected cells.