We present a method for estimating the asymptotic stability region(ASR) of uncertain variable structure systems with bounded switching feedback controllers. Using linear matrix inequalities(LMIs) we estimate the ASR and we show the exponential stability of the closed-loop control system in the estimated ASR. We also give a simple LMI-based method for designing switching surfaces that will make the estimated ASR big. Finally, we give numerical examples in order to show the effectiveness of our method.