This paper presents the results of the investigation concerning the stability of the motion of a connecting rod. For simplicity in analysis, the rod is assumed to have a constant cross-sectional area. In the analysis a perturbation method was used, based on the assumption that the ratio of crank radius to the rod length is a small parameter. The successive approximations to the transverse motion of the rod satisfying the Mathieu-type of partial differential equations, from which expressions for instability regions of motion were derived. Numerical method was used in calculating several cases of the transverse vibrational response, both stable and unstable.