To avoid complicated computation, analytical solution of the energy-minimization multi-scale (EMMS) model for heterogeneous particle-fluid two-phase flow has been derived through analyzing the suspension properties of clusters, thus allowing local hydrodynamics, choking Velocity and saturation carrying capacity to be conveniently calculated without recourse to complex mathematical algorithm. It not only greatly simplifies the formulation of the EMMS model but also makes the computation of the model converge more easily to its solution, and therefore greatly facilitates the application of the EMMS model. In addition, some confusion on extremum energy in fluid-particle two-phase flow is also clarified by recapitulating the EMMS model.