Photoisomerization kinetics of trans 4-methoxystilbene induced by irradiation with linearly polarized light was investigated in the glassy state of poly(methyl methacrylate)(PMMA). The reaction was strongly selected by linearly polarized light as revealed by a large dichroic absorption generated upon irradiation. The optical anisotropy increases with increasing irradiation time and passes through a maximum before approaching an equilibrium value, which strongly depends on the experimental temperatures. From the decay of the total absorbance of the trans-isomer observed upon irradiation with 313 nm UV light, it was found that the rates of the photoisomerization trans --> cis were not significantly changed within the temperature range of the experiments. On the other hand, the reorientational relaxation times of the stilbene, which were directly measured by the annealing-after-irradiation techniques, depend strongly on temperature. These relaxation data were compared to the previous results obtained with dopants of the size larger than the stilbene and were discussed in conjunction with the local relaxation processes of the PMMA matrix.