A theoretical analysis of the effects of permeability and the injection/suction on an oscillatory free convective flow of a viscous incompressible fluid through a highly porous medium bounded between two infinite vertical porous plates is presented. The entire system rotates about the axis normal to the planes of the plates with uniform angular velocity . For small and large rotations the dependence of the steady and unsteady resultant velocities and their phase differences on various parameters are discussed in detail.