Many approaches to elastography incorporate shear waves; in some systems these are produced by acoustic radiation force (ARF) push pulses. Understanding the shape and decay of propagating shear waves in lossy tissues is key to obtaining accurate estimates of tissue properties, and so analytical models have been proposed. In this paper, we reconsider a previous analytical model with the goal of obtaining a computationally straightforward and efficient equation for the propagation of shear waves from a focal push pulse. Next, this model is compared with an experimental optical coherence tomography (OCT) system and with finite element models, in two viscoelastic materials that mimic tissue. We find that the three different cases-analytical model, finite element model, and experimental results-demonstrate reasonable agreement within the subtle differences present in their respective conditions. These results support the use of an efficient form of the Hankel transform for both lossless (elastic) and lossy (viscoelastic) media, and for both short (impulsive) and longer (extended) push pulses that can model a range of experimental conditions.