The temperature dependence of the longitudinal elastic constants c(22), c(33), and of the transverse elastic constant c(44), as obtained by Brillouin spectroscopy, reveals an unexpected elastic behavior in CuGeO3 prior to the spin-Peierls magnetic transition (T(SP)approximate to 14 1 K) At room temperature c(33)much greater than c(44)>c(22). Below about 50 K a steep increase in the values of the longitudinal elastic constants leads to a crossover of the values of c(22) and c(44) with c(22)>c(44). The existence of translation-rotation coupling in CuGeO3 could account for the elastic behavior above T-SP. The anisotropy of the magnetoelastic coupling at the spin-Peierls transition temperature is reflected in the different temperature behavior of the elastic constants (c(33), c(44), and c(22)) at T(SP)approximate to 14.1 K.