This paper describes the propagation of shear waves in a Holzapfel-Gasser-Ogden (HGO) material and investigates the potential of magnetic resonance elastography (MRE) for estimating parameters of the HGO material model from experimental data. In most MRE studies the behavior of the material is assumed to be governed by linear, isotropic elasticity or viscoelasticity. In contrast, biological tissue is often nonlinear and anisotropic with a fibrous structure. In such materials, application of a quasi-static deformation (pre-deformation) can influence plays an important role in shear wave propagation. Closed form expressions for shear wave speeds in an HGO material with a single family of fibers were found in a reference (undeformed) configuration and after an imposed pre-deformation in simple shear. These analytical expressions show that shear wave speeds are affected by the parameters (µ_0,k_1,k_2,?) of the HGO model and the direction and amplitude of the pre-deformation shear, ?. Simulations of corresponding finite element models confirm the predicted influence of HGO model parameters on speeds of shear waves with specific polarization and propagation directions. Importantly, closed-form expressions for the wave speed in terms of the parameters of the HGO model will allow efficient estimation of material parameters from experimental data.