Understanding the solid conveying process is important for the optimal design of micro injection molding machines. To solve problems such as starve feeding and process instability during plastication of polymers, which deteriorate product qualities, studies have been carried out on the conveying process of discrete polymer pellets. The effect of screw axis inclination on the speed of solid conveying is investigated with both simulation and experimental approaches. A discrete element modeling method (DEM) specially designed for simulating polymer particle movements in screw channels, which takes into account the effect of gravity while maintaining the simplicity of calculations, has been developed. The agreements between results of simulations and experiments verify the integrity of the models developed herein. The proposed modeling method is capable of optimizing the design of plasticizers of micro injection molding machines.