The long wavelength, low-frequency modes of motion are the relevant motions for understanding the continuum mechanical properties of biomolecules. By examining these low-frequency modes, in the context of a spherical harmonic basis set, we identify four elastic moduli that are required to describe the two-dimensional elastic behavior of capsids. This is in contrast to previous modeling and theoretical studies on elastic shells, which use only the two-dimensional Young's modulus (Y) and the bending modulus (κ) to describe the system. Presumably, the heterogeneity of the structure and the anisotropy of the biomolecular interactions lead to a deviation from the homogeneous, isotropic, linear elastic shell theory. We assign functional relevance of the various moduli governing different deformation modes, including a mode primarily sensed in atomic force microscopy nanoindentation experiments. We have performed our analysis on the T = 3 cowpea chlorotic mottle virus and our estimate for the nanoindentation modulus is in accord with experimental measurements.