Chemotaxis is an important process in a plethora of biological and medical processes such as bacterial aggregation, wound healing, and cancer tumor growth and metastasis. In the case of cancer growth and metastasis, the role of chemotaxis is twofold. Firstly it promotes the vascularization of the tumor by provoking angiogenesis to create a blood circulatory-feeding network for the cancer cells. Secondly it directs the migration of metastating cancer cells into the circulatory system which allows these cancer cells to reach other parts of the organism. Deterministic mathematical modeling of biological processes during the growth and metastasis of the cancer has been done mostly by means of reaction-diffusion-chemotaxis equations. In our recent project we have done an intensive numerical study of the multi-species and multi-chemoattractants chemotaxis system. We have developed an efficient, second order, stable and robust finite volume-finite difference scheme. In the present project we will generalize and extend the already developed numerical method from the case of multi-species, multi-chemoattractants bacterial chemotaxis to the case of cancer cell proliferation and metastasis. More specifically, the aim is a) to develop an efficient, finite volume scheme for models describing chemotactic response of cancer cells, and b) to compare the numerical results with existing experimental data.