In present study, the interaction between internal solitary waves (ISWs) and a uniform slope is numerically studied based on the moving particles semi-implicit (MPS) method. Aiming at the stratified flows, a multiphase MPS method is firstly developed on the basis of the original single-phase MPS method, by introducing a series of special interface treatments. These treatments include the density smoothing scheme, inter-particle viscosity model and surface tension model. Then, the multiphase MPS method is validated through the numerical simulation of the ISWs generation and propagation. The results obtained by present method achieve good agreement with the experimental data and other numerical methods on the interfacial displacements and wave profiles. Moreover, the calculated pressure and velocity fields are smooth and reflect the actual physical features. Finally, the multiphase MPS method is applied to investigate the ISWs interaction with the submarine slopes with different inclinations, and a qualitatively analysis of the different breaking mechanisms is performed.