The Cell Mapping method is a robust tool for investigating nonlinear dynamic systems. It is capable of finding the attractors and corresponding basins of attraction of a system under investigation. To investigate the applicability of the Cell Mapping method to discontinuous systems, a forced zero-stiffness impact oscillator is chosen as an application. The numerical integration algorithm, the basic element in the Cell Mapping method, is adjusted to overcome the discontinuity. Four types of Cell Mapping techniques are applied: Simple Cell Mapping, Generalized Cell Mapping, Interpolated Cell Mapping, and Mixed Cell Mapping. The last type is a new modification to existing types. Each type of Cell Mapping is briefly explained. The results are compared to the exact solutions. The Interpolated Cell Mapping and Mixed Cell Mapping methods are found to produce the most accurate results for this case.