Continuing advances in genomics, molecular and cellular mechanobiology and immunobiology, including transcriptomics and proteomics, and biomechanics increasingly reveal the complexity underlying native tissue and organ structure and function. Identifying methods to repair, regenerate, or replace vital tissues and organs remains one of the greatest challenges of modern biomedical engineering, one that deserves our very best effort. Notwithstanding the continuing need for improving standard methods of investigation, including cell, organoid, and tissue culture, biomaterials development and fabrication, animal models, and clinical research, it is increasingly evident that modern computational methods should play increasingly greater roles in advancing the basic science, bioengineering, and clinical application of regenerative medicine. This brief review focuses on the development and application of computational models of tissue and organ mechanobiology and mechanics for purposes of designing tissue engineered constructs and understanding their development in vitro and in situ. Although the basic approaches are general, for illustrative purposes we describe two recent examples from cardiovascular medicine—tissue engineered heart valves (TEHVs) and tissue engineered vascular grafts (TEVGs)—to highlight current methods of approach as well as continuing needs.