This study examines the numerical solution of two-phase problems using the reduced Kapila model, that is, the four-equation model. This model was tested on different test cases using the HLLC numerical scheme and its extensions. The results reveal that most reconstruction strategies produce results that are in good agreement with the reference solutions. However, certain discrepancies have also been found. This work is preliminary to validate the capabilities of the NSMB solver for two-phase flows and is intended to pave the way for other two-phase flow models planned to be added to the solver.