We present a vibrational electron energy loss spectrum (EELS) of neat solid methane, with partially resolved bands for nu(4) and nu(2) excitations. The intensities of the observed bands are well reproduced by scattering calculations performed by the recently developed cubic-grid Gaussian basis set (CGGBS) method. For testing the CGGBS method we also used literature data on elastic electron scattering by methane and data on elastic and vibrational inelastic electron scattering by H-2 and H2O. We present a procedure for the analytical differentiation of the scattering amplitude with respect to normal coordinates.