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In this study, liquid-liquid-solid three phase mixture flow through the pipe have been investigated. A differential equation system representing the steady state flow has been solved analytically with D'Alambert methods; formulas for the local velocities of the mixture phase have been obtained. The unsteady state flow of this mixture was also solved numerically by using finite difference equation method. Local velocity-time graphics has been obtained to see the phase in steady flow progress. The analytical and numerical solution results of steady state flow are compared by plotting local velocity graphs for different radiuses. It was obtained that the velocity profiles from both of the solutions are identical. [ABSTRACT FROM AUTHOR]