The induced flow of an incompressible, unbounded fluid is considered when a circular cylinder performs small transverse and torsional oscillations. An analytic solution, valid into the inner layer provides the necessary conditions for the matching with the numerical solution at the outer layer. The results are compared with those of the single transverse oscillation. It is shown that the torsional oscillation significantly affects the depth of the boundary layer and the position of the jet axis, especially when its amplitude becomes larger.