High-speed planetary mixers can rapidly and efficiently combine rheological liquids, such as polymer resins and paste materials, because of the large centrifugal forces generated by the planetary motion of the mixing vessel. Only a few attempts have been made to computationally model and analyze the intricate mixing patterns of highly viscous substances. This paper presents meshless flow simulations of the planetary mixing of polymeric fluids. This research utilized the smoothed particle hydrodynamics (SPH) approach for numerical calculations. This method has advantages over the finite-volume method, which is a grid-based computational technique, when it comes to modeling interfacial and free surface flow problems. Newtonian rheology and interfacial surface force models were used to calculate the dissipative forces in the partial differential momentum equation of fluid motion. Simulations of the flow of an uncured polyurethane resin were carried out while it was mixed in a planetary mixer, under various operating conditions. Simulations using SPH were able to accurately reproduce the intricate flow and blending pattern, providing insight into mixing mechanics and mixing index evolution characteristics according to operating conditions for the planetary mixing of polymeric fluids. The simulation results showed that the spiral band, which promotes the mixing performance, is densely and distinctively formed under high-speed operation conditions.