Consider an infinite expanse of a porous medium where in we assume a viscous fluid flow governed by Brinkman equations. We assume that in the medium there is a solid oblate spheroid past which there is a uniform flow along the axis of symmetry of the spheroid. We obtain expressions for velocity components and pressure of the flow field in terms of Legendre functions, radial and angular spheroidal wave functions. We obtain an expression for the drag experienced by the oblate spheroid and numerically evaluate the drag for different values of the permeability of the medium and varying size of the spheroid. The variation of the drag is presented through graphs.