In this paper, the development of a solver for the Multi-Fluid and Multi-Pressure model (MFMP) is presented. MFMP is the extension of the two-fluid model. In this model, the number of fluids can be greater than or equal to two. The fluids are considered to be in mechanical nonequilibrium. The pressure across the interface is not considered to be equal. A pressure-based and semi-implicit numerical method is proposed. This is different from the method used for the two-fluid model or single-pressure model. The solver is verified by classical two-fluid benchmark problems and multifluid problems. The Multi-Fluid and Single-Pressure model (MFSP) and MFMP are used. Bestion’s model is used in MFMP to consider the nonequilibrium effect of pressure. The computation shows that MFSP is unstable if the number of meshes is large enough, while MFMP is stable for the two-fluid problems and most cases of the multifluid problems. The results of MFMP are in agreement with the reference solution or analytical solution for the two-fluid problems and reasonable for most cases of the multifluid problems.