Methods of numerical analysis of gas-particle flows is classified into micro, meso and macro scale approaches based on the concept of multi-scale mechanics. Next, discrete particle simulation which belongs to the micro-scale approach for the particle phase is explained. The author focusses on dense phase flows where particle-to-particle interaction has significant effects on the overal behavior of phenomena. To treat the particle-to-particle interaction mathematically, techniques named DEM (Distinct Element Method) and DSMC (Direct Simulation Monte Carlo) have been developed. DEM is useful for the contact -dominated flows and DSMC method for the collision-dominated flows. Combining DEM or DSMC with CFD (computer fluid dynamics), the discrete particle simulation becomes a more practical tool for industrial flows because not only the particle-particle interaction but particle-fluid interaction can be handled. Various examples of simulations are shown; such as dense phase pneumatic conveying, spouted bed, dense phase fluidized bed, fast circulating fluidized bed and so on.