The elastic moduli in anisotropic media can be estimated using either direct mechanical or sound speed measurements. Here we compare moduli in the passive heart estimated with different methods and demonstrate that high-frequency (i.e., ultrasonic) sound speed measurements are inconsistent with static deformations and low-frequency shear wave results. Both tissue fixation and the high-operating frequency of ultrasonic measurements contribute to these discrepancies. Moreover, the precision of ultrasonic sound speed measurements required to estimate elastic moduli describing static deformations of a nearly incompressible anisotropic medium such as the heart appears to be beyond the scope of current methods. We conclude that an incompressible anisotropic elastic model is appropriate for elasticity reconstruction in the heart, in which three independent constants characterize small strain behavior, but four are needed for a fully nonlinear description of finite deformations.