In this note, the problem of estimating the asymptotic stability region (ASR) of uncertain systems with bounded sliding mode controllers is considered. To simplify the problem me use a state transformation and choose a suitable Lyapunov function for the transformed control system. Using the Lyapunov function we estimate the ASR and show the exponential stability of the closed-loop control system in the region. Also, by an example we show that for a certain class of uncertain dynamical systems with bounded sliding mode controllers our method gives a more improved estimate of the ASR.