Mechanical properties of the myocardium have been investigated intensively in the last four decades. Many complex strain energy functions have been used to estimate the stress-strain relationship of myocardium because the heart muscle is an inhomogeneous, anisotropic, and nearly incompressible material, which undergoes large deformations. These functions can be effective for fitting in vitro experimental data from myocardial stretch testing. However, it is difficult to model in vivo myocardium using these strain energy functions. Moreover, such estimates have so far been carried out almost exclusively on the left ventricle, because of the relative thinness and complex geometry of the right ventricle. Previous work from our research group has successful estimated the motion and deformation of both the left and the right ventricles, using data from noninvasive tagged magnetic resonance imaging. In this paper, we present a novel statistical model to estimate the in vivo material properties and strain and stress distribution in both ventricles, using such data. Two normal hearts and two hearts with right-ventricular hypertrophy (RVH) were studied and noticeable differences were found between the strain and stress distributions for normal volunteers and RVH patients. Compared to the strain energy function approach, our model is more intuitively understandable.