Abstract: A method of the exact Riemann solver was studied to be widely used in multi-fluids, such as pure fluid,non-conservative two phase fluids,as well as the elastic-plastic flows. Firstly, the continuous hyperbolic character of hydro-mechanical partial differential eguation was analyzed based on the characteristic theory. Then, the full wave structure of the Riemann solver was obtained from its right characteristic values. Finally, a disconnected relation formula of the full wave system was developed to establish the Riemann solver automatically. Results show that, the Riemann solver possesses full wave structure of the Riemann problem, includes all mathematics properties of the continuous system, and can obtain the exact physical values across the waves. When it is used in the Lagrangian method or the ALE ones to solve the multi-material problems, the Riemann solver obtains the exact values from the coming wind, shows a high accuracy and less dissipation. Numerical experiments in two-phase flows or the elastic-plastic flows validate the merits and characteristics of the Riemann solver.