A 3D three-equation linear spring-dashpot model considering the normal contact force, the tangential contact force, and the rolling friction torque, and the corresponding programs for granular dynamics were developed. The flow and the segregation of the S-type binary granular mixtures in a thin rotating horizontal drum were simulated by using the new model. The influences of the rotation speed and the load of the drum on the pattern formation were discussed. The simulation results show that the pattern formation of the S-type binary granular mixtures in the rotating drum can be predicted accurately. As the rotation speed is high, the moon pattern appears,in which the small particles concentrate in a central core and the large particles distribute in the periphery. As the rotation speed is lowered, the petal pattern is found in thin drums, and the number of petals increases as the rotation speed decreases. The process of pattern formations was obtained by the simulation. As the petal pattern forms, the wavy flow of granules in the drum appears. Finally, the necessary condition and mechanisms of the pattern formation in the thin drums are discussed in the paper.