Abstract <p>A mathematical model of viscous fluid flow induced by the rotational-oscillatory motion of a submerged porous spherical shell with a spherical gas cavity is considered. In the Stokes approximation, analytical solutions are obtained for the time-dependent Brinkman equation that describes viscous fluid flow in the porous medium and the Navier–Stokes equation that describes viscous fluid flow outside the porous medium. An analysis of the obtained mathematical model is given. The case of uniform rotation about a fixed axis of the porous spherical shell with a spherical gas cavity inside it in a viscous fluid is considered.</p>