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Some chemically peculiar stars in the upper main sequence show rotational period variations of unknown origin. We propose that these variations are a consequence of the propagation of internal waves in magnetic rotating stars that lead to the torsional oscillations of the star. We simulate the magnetohydrodynamic waves and calculate resonant frequencies for two stars that show rotational variations: CU Vir and HD 37776. We provide updated analyses of rotational period variations in these stars and compare our results with numerical models. For CU Vir, the length of the observed rotational period cycle, | $\mathit {\Pi }=67.6(5)$ | yr, can be well reproduced by the models, which predict a cycle length of 51 yr. However, for HD 37776, the observed lower limit of the cycle length, | $\mathit {\Pi }\ge 100$ | yr, is significantly longer than the numerical models predict. We conclude that torsional oscillations provide a reasonable explanation at least for the observed period variations in CU Vir.