The aim of this paper is to determine the exact solutions for the velocity field related to the magnetohydrodynamic (MHD) and rotating flow of a second grade fluid in a porous medium induced by accelerated flows over an oscillating plate. This is accomplished by using the Fourier sine and Laplace transforms. Two explicit flow situations of the fluid are considered. In each case, both sine and cosine oscillations of the plate are incorporated. Finally, some graphical results of the fluid's velocity profiles are presented correspondingly for different values of the emerging parameters. The physical interpretations for these parameters are discussed with the help of these graphical illustrations. © 2011 Academic Journals.