Formation of optical anisotropy under linearly polarized light has been studied in films of poly(n-butyl methacrylate) and poly(n-hexyl methacrylate) doped with azo compound (1-naphthyl-p-azo-methoxybenzene). Time profiles of the absorption anisotropy and absorbance can not be fitted with a commonly used model of anisotropy formation, which includes the transition dipole turns upon cis-trans isomerization and the rotational diffusion: the experimental values of anisotropy happen to be much lower than the calculated ones. To explain the low anisotropy level, fast molecular librations, i.e., stochastic pendulum-like oscillations of azo molecules about their average orientations were introduced. Numerical simulation of anisotropy and absorbance time profiles with the modified model gives estimates for average libration amplitude of 45-60 degrees at temperatures 25-65 K below T-g.