Influence of objective corotational rates to shear oscillation is discussed here under the framework of finite deformation, \(J_ 2\)-flow theory. Under an elastic-plastic, mixed hardening constitutive law, the active stress \(s\) and back stress \(b\) are shown to be governed by two sets of equations formally uncoupled to each other. Formal solutions of complex stresses are obtained for plane strain, isochoric deformation, with the conclusion that the shear oscillation behavior for an elastic- plastic solid can be asymptotically reduced to a rigid-plastic solution and a higher order correction, provided the initial shear strain is small.