Unsteady motions of 2-dimensional reactive flows have been simulated to investigate the hydrodynamic effect and the diffusive-thermal effect on the instability of freely expanding cylindrical flames. The numerical model includes compressibility, viscosity, heat conduction, molecular diffusion, one-step chemical reaction, and convection. We obtained the growth rates of disturbances superimposed on the cylindrical flames depending on their wave numbers. The results showed that the growth rates in the cylindrical flames are consistent with those in the plane flames for the case where the Lewis number is unity. Therefore, the hydrodynamic effect on the flame instability is independent of the mean curvature of the front. When the Lewis number is smaller/larger than unity, the growth rates in the cylindrical flames are lower/higher than those in the plane flames. It means that the instabilizing/stabilizing influence of the diffusive-thermal effect is less in the cylindrical flames than in the plane flames.