Semicrystalline polymer materials play an essential role in the industry, such as the polyetheretherketone (PEEK) for the F1 engine components and the polytétrafluoroéthylène (PTFE) for corrosion resistant lining of pipes. The modeling and prediction of polymer microstructures has environmental and economic interests. In this study, a mesoscale modeling of spherulite pattern formation is constructed. For this purpose, the spherulite growing is modeled by a multi-phase fields model and by a cellular automaton. The spherulite nucleation is modeled using the concept of random local nucleation time. The kinetics parameters of nucleation and crystal growth rate are identified from PESU experimental data. The generated microstructures are used to study the elastic anisotropy at the mesoscopic scale.