Heart valve diseases are some of the most prevalent modern maladies, with more than 5 million cases diagnosed in America each year. These complex diseases vary in affliction mechanism but are correlated with changes to the leaflet mechanics and impairment of valve function. Three-dimensional computational modeling has recently been employed by our group to gain insight into how disease-induced stress overloads affect the underlying structure and tissue mechanics during cardiac function. To enable these models to emulate physiological deformations, accurate material data regarding the mechanical response of the valve leaflets must be fit with appropriate constitutive models. In this study, our group elucidated the tissue response of each leaflet from healthy porcine mitral and tricuspid valves (n = 6 each) through force-controlled planar biaxial testing with five physiologically-valid loading protocols. Each leaflet demonstrated a distinct but characteristically nonlinear and anisotropic response, with the tissue stretches on average 30.7% higher in the radial than circumferential direction under equibiaxial systolic loading. The material response data for each leaflet was fit to a variety of constitutive models, both phenomenological and structural. Base parameters for the strain energy functions for each leaflet were optimized through an inverse finite element modeling approach, by initializing parameters and running simulations to produce a convergent solution. Through comparison of the model-predicted leaflet deformations with the observed tissue deformations in testing, improved constitutive models were obtained and are expected to improve the fidelity and utility of atrioventricular valve models in disease diagnosis and treatment.