Aiming at the non-smooth characteristics of the non-smooth devices/circuits, a modeling and simulation method based on the standard mathematical programming problem is proposed. Firstly, the non-smooth device is modeled as a Piecewise Linear(PWL) function with a possible state jumping. Secondly, some dynamic system equations of the non-smooth linear characteristic of the circuit formed by the non-smooth devices are given. Then, the time discretization is applied to these non-smooth dynamic system equations, and various types of one-step non-smooth problems are yielded, such as (linear) complementary problems or nonlinear(or quadratic) programming with equation-inequality constraints. The numerical solution is carried out. The simulation results show that the proposed numerical modeling method is effective for non-smooth systems with a large number of events and is robust to the variation of model parameters.