The internal dynamics of L-alanine in the crystal environment were investigated using molecular dynamics simulations and normal mode calculations. Detailed results are presented for the rotational motion of the methyl and ammonium groups. The rotational barriers and librational frequencies are found to be significantly higher in the crystal than in the isolated molecule. Librational power spectra, calculated from the molecular dynamics simulations by Fourier transformation of the velocity autocorrelation function agree well with the forms and frequencies of the normal modes if the periodic box size used is large enough to avoid unphysical correlations.