The nanoindentation response of empty viral capsids is modeled using three-dimensional finite element analysis. Simulation with two different geometries, spherical and icosahedral, is performed using the finite element code Abaqus. The capsids are modeled as nonlinear Hookean elastic, and both small and large deformation analysis is performed. The Young's modulus is determined by calibrating the force-indentation curve to data from atomic force microscopy (AFM) experiments. Force-indentation curves for three different viral capsids are directly compared to experimental data. Predictions are made for two additional viral capsids. The results from the simulation showed a good agreement with AFM data. The paper demonstrates that over the entire range of virus sizes (or Foppl-von Karman numbers) spherical and icosahedral models yield different force responses. In particular, it is shown that capsids with dominantly spherical shape (for low Foppl-von Karman numbers) exhibit nearly linear relationship between force and indentation, which has been experimentally observed on the viral shell studies so far. However, we predict that capsids with significant faceting (for large Foppl-von Karman numbers) and thus more pronounced icosahedral shape will exhibit rather nonlinear deformation behavior.