A study on the constitutive models of tumor tissues is critical for the advancement of computational tools for clinical diagnosis and treatment plans. In this respect, continuum based constitutive models of tumor tissues applied in the computational analysis of tumor tissues are reviewed in this work. An introduction to the continuum based computational modeling of tumor tissue and a brief review of the applications of computational models in tumor diagnosis and treatment plans are presented in Sec. 1. The pathophysiology of tumor is given in Sec. 2. Continuum based constitutive models of tumor tissues are reviewed in Sec. 3 and in Sec. 4, conclusions and recommendations for the future development of tumor constitutive model are presented. It is the aim of the authors to provide a comprehensive study on the various constitutive models of tumors to enhance the application of biomechanical simulation of tumor tissues.