This paper proposes a new model for state-dependent delay systems, which arise in various fields. After discretization and state augmentation to include the past history, the delay term is represented by using a nonlinear gain whose element is a piecewise linear function of the state. Thus the model becomes nonlinear but finite dimensional. The SOS (Some Of Squares) technique is then applied to analyze stability of this system. Numerical simulation is carried out to illustrate the effectiveness of the proposed method.