In this paper we present the governing equations for the flow of a dense particulate mixture in a pipe. The governing equations for the individual constituent as well as the mixture are provided based on continuum mechanics. Constitutive relations for the stress tensors and the interaction force are presented and discussed. A model is provided for the viscosity of the mixture. Numerical solution for the steady fully developed isothermal flow of such a mixture in a pipe is presented. The importance of the pressure drop and the skin friction in pipe flow are also discussed.