This contribution presents a novel constitutive model for rate-dependent response of the passive myocardium. As a first step, we performed a comparative study on dispersion-type anisotropic hyperelastic constitutive models [1–3] and assessed performance of various density distribution functions by fitting to experiments conducted on three distinct tissues . Next, we proposed an angular integration type anisotropic viscoelastic constitutive model that uses bivariate von-Mises distribution function to capture fiber dispersion in passive myocardium. The baseline hyperelasticity is described by a generalized structure tensor formulation proposed by GASSER ET AL. . The non-equilibrium part of the model utilizes a quadratic free energy function in the logarithmic strain space and a power-type nonlinear evolution equation in orientation directions. The overstress response is then obtained by the numerical integration over the unit sphere by making use of 21 quadrature points. The proposed model parameters are obtained from cyclic triaxial shear and triaxial shear relaxation experiments on human passive myocardium .