ABSTRACT In this paper we present a mathematical model of the tumor development, tumor cells movement and cell–matrix interactions. This model is considered tumor cells, concentration of oxygen, concentration of nutrient, changes in their microenvironment (tumor angiogenic factors (TAF), extracellular matrices (ECM)) and their matrix of blood vessels, expressed by a chain of discrete tips. With this mathematical model and the results of numerical simulation, the cell properties are closely individual-based cell interactions, can affecting the tumor shape, the tumor’s final structure and also discussed which of these interactions is perhaps tumor cells are discrete. Also we described the procedure of tumor development and the changes in microenvironment from avascular to vascular phase, indicating that the matrix of blood vessels develops step by step as the tumor grows.