Shear Wave Elastography (SWE) has been proposed to investigate cardiac health by non-invasively monitoring tissue stiffness. Previous work has shown that the plate-like geometry of the Interventricular Septum (IVS) may result in a dispersion similar to Lamb waves, complicating the link between shear wave speed and cardiac stiffness. However, the IVS is not a simple plate, e.g., its thickness tapers across its length. We have used 2-D Finite Element simulations to investigate the effects of tapering on Lamb waves. The model consists of an elastic slab immersed in water, with a thickness decreasing smoothly in space from 9 to 3 mm. Pulses with low (0–80 Hz) and high (0–700 Hz) frequency contents were used to excite natural and acoustic radiation force induced waves. The results show that, at the lower frequencies, propagation speed can decrease during propagation by ~20% due to the thickness reduction, producing a nonlinear space-time relation from which multiple speed values can be extracted. At higher frequencies, the main observation is a dependence of the dispersion behavior on the shape of the tapering (e.g., linear, concave, or convex). These results suggest that septal geometry is likely to play a role in deriving cardiac stiffness from propagation speed measurements.