Physics-based lithium ion models are widely used to predict the electrochemical behavior of lithium ion cells. The implementation of such a model typically requires solving a diffusion problem in solid particles. A linear time-invariant (LTI) model is proposed for the solid-phase diffusion problem. This LTI model can be used for spherical and non-spherical particles. For spherical particles, results from using the LTI model are compared with those from solving full diffusion equation, and excellent agreement is achieved. The LTI model solves only a few equations, and thus it runs much faster than the model solving the full diffusion equation. Impact of particle shapes on the electrochemical behavior is investigated after the model is validated.