This paper analyzes the transient stability of power systems with uncertain parameters. More precisely, we suppose that the inertia constants and damping coefficients of generators are uncertain, and consider the problem of checking the stability of an equilibrium state for all possible values of the uncertain parameters, and estimating the intersection of the region of attraction for those parameter values. By using a polytope representation for the uncertain parameters, we present a method to solve the problem. In the presented method, we solve a sum of squares (SOS) programming problem based on the polytope representation. It is proven that if this SOS programming problem is feasible, then our method provides a solution to the analysis problem of the transient stability.