Using a damped mass-spring model, we simulate wobble of spinning homogeneous viscoelastic ellipsoids undergoing non-principal axis rotation. Energy damping rates are measured for oblate and prolate bodies with different spin rates, spin states, viscoelastic relaxation time-scales, axis ratios, and strengths. Analytical models using a quality factor by Breiter et al. and for the Maxwell rheology by Frouard & Efroimsky match our numerical measurements of the energy dissipation rate after we modify their predictions for the numerically simulated Kelvin–Voigt rheology. Simulations of nearly spherical but wobbling bodies with hard and soft cores show that the energy dissipation rate is more sensitive to the material properties in the core than near the surface.