The rotating magnetohydrodynamics (MHD) flow of a second grade fluid due to an accelerated plate is examined. Modified Darcy's law is used to formulate the physical problem in a porous space. Two cases of interest namely constant and variable accelerated MHD flows are addressed. Fourier sine transform technique is adopted to solve analytically the resulting problems. Finally, from the exact solutions the implied effects of emerging flow parameters on the velocity field are displayed and discussed.