In this study, a physics-based model for light punch through (LPT) carrier stored trench bipolar transistor (CSTBT) is developed. The model is based on the Fourier series solution of ambipolar diffusion equation implemented in MATLAB and Simulink. In the model, the MOS-side two-dimensional (2D) effects resulting from trench gate and carrier storage layer are studied analytically. Assuming high-level injection in LPT buffer layer, the model also describes the carrier transport, redistribution and recombination in the buffer layer in details. The static and transient experiments for a commercial CSTBT are used to validate the presented model. The simulation results are compared with experiment results and good agreement is obtained.