The myocardium is known to be an anisotropic medium where the muscle fiber orientation changes through the thickness of the wall. Shear wave elastography methods use propagating waves which are measured by ultrasound or magnetic resonance imaging (MRI) techniques to characterize the mechanical properties of various tissues. Ultrasound- or MR-based methods have been used and the excitation frequency ranges for these various methods cover a large range from 24-500 Hz. Some of the ultrasound-based methods have been shown to be able to estimate the fiber direction. We constructed a model with layers of elastic, transversely isotropic materials that were oriented at different angles to simulate the heart wall in systole and diastole. We investigated the effect of frequency on the wave propagation and the estimation of fiber direction and wave speeds in the different layers of the assembled models. We found that waves propagating at low frequencies such as 30 or 50 Hz showed low sensitivity to the fiber direction but also had substantial bias in estimating the wave speeds in the layers. Using waves with higher frequency content (>200 Hz) allowed for more accurate fiber direction and wave speed estimation. These results have particular relevance for MR- and ultrasound-based elastography applications in the heart.