This paper considers local stability analysis of the systems with input saturation via polynomial programming. First, describing the saturated inputs in terms of logic variables, we derive a local stability condition with the aid of generalized S-procedure of polynomials with higher degree of freedom. Then, we obtain a Lyapunov function using Sum of Squares decomposition, which specifies the region of attraction. Moreover, it is shown that the method can be easily extended to the case where piecewise quadratic Lyapunov functions are adopted. Finally we demonstrate its effectiveness through numerical examples.