New approach to simulation of continuous and discrete Land Mobile Satellite communication Channel (LMSC) is considered. The main topic addresses modeling of the fading and shadowing of the received signal as correlated non-Gaussian Markov processes, generated by corresponding nonlinear Stochastic Differential Equations (SDE). Simulation of the continuous LMSC conceptually coincides with the two-state Propagation model, known as the most effective in the scenario considered. The new model stands in a very good fit with all previous results, both modeled and stored from the real channel. It also resolves almost all disadvantages of the previous approaches: limitations in random process generation and discontinuity of the fading process at the state transfers.