Tumor induced angiogenesis is the bridge between benign and malignant tumor growth stages. In this process, growth and migration of endothelial cells build capillaries to supply the tumor with blood for its further growth. Regarding the importance of capillary formation and blood flow in angiogenesis, simulation of this phenomenon plays important role in tumor growth and cancer development studies. In this work, considering intracellular, cellular, and extracellular scales a mathematical model of tumor-induced angiogenesis is used to consider mechanical effects of extracellular matrix on growth and migration of endothelial cells. These effects are matrix density and its fiber length. In this study, to model cellular dynamics, a discrete lattice based Monte Carlo method is used. Results show that migration of endothelial cells and development of capillaries are possible in a specified range of matrix density and matrix fiber length. Based on the results, medium matrix densities and low fiber length provide a suitable environment for capillaries growth and development. The model is a promising tool for modeling tumor induced angiogenesis and is a base for development of models for loop formation and blood flow in capillaries around tumor.