The flow generated by a circular cylinder, performing longitudinal and torsional oscillations, in an infinite expanse of a micropolar fluid is studied. Analytical expressions for the velocity and micro rotation components are obtained using no slip and hyper stick conditions at the boundaries. The effects of coupling number, Reynolds number and gyration parameter on the transverse and axial velocity components are shown and explained graphically. Also explicit expression for the drag force acting on the wall of the cylinder is derived and the effects of pertinent parameters on the drag are shown graphically.