Tissue engineering represents a promising technique to overcome the limitations of the current valve replacements, since it allows for creating living autologous heart valves that have the potential to grow and remodel. However, also this approach still faces a number of challenges. One particular problem is regurgitation, caused by cell-mediated tissue retraction or the mismatch in geometrical and material properties between tissue-engineered heart valves (TEHVs) and their native counterparts. The goal of the present study was to assess the influence of valve geometry and tissue anisotropy on the deformation profile and closed configuration of TEHVs. To achieve this aim, a range of finite element models incorporating different valve shapes was developed, and the constitutive behavior of the tissue was modeled using an established computational framework, where the degree of anisotropy was varied between values representative of TEHVs and native valves. The results of this study suggest that valve geometry and tissue anisotropy are both important to maximize the radial strains and thereby the coaptation area. Additionally, the minimum degree of anisotropy that is required to obtain positive radial strains was shown to depend on the valve shape and the pressure to which the valves are exposed. Exposure to pulmonary diastolic pressure only yielded positive radial strains if the anisotropy was comparable to the native situation, whereas considerably less anisotropy was required if the valves were exposed to aortic diastolic pressure.