Free rotating chain (FRC) is a well-known model of polymer but the knowledge to its mechanical property is yet incomplete. This work uses Monte Carlo simulation to evaluate the relation between force and extension, the specific heat, the stretching strength and the fourth-order cumulants of the order parameter of a three-dimensional (3D) FRC. We simplify some expressions to calculate the thermodynamical quantities. Our results reveal that at low force, the behavior of the mechanical property of the model is the same as that of a free jointed chain (FJC) in both two-dimensional (2D) and 3D cases. But beginning from a moderate force, the two models have different mechanical properties. Moreover, we find that a 3D FRC has essential different mechanical property from its 2D counterpart, because the extension of a stretched 2D FRC can subject to a first order transition when the bond angle is large enough, but there is no such a transition for a 3D chain despite its stretching strength exhibits a peaks at large bond angle. Our findings reveal that the space constraint on a stretched polymer favors a sharp change in its size.