The motion of binary particles in three horizontal rotating drums with continuous rotational speed changes was studied based on the Discrete Element Method (DEM). Different simulation conditions were compared between two circular drums and an elliptical drum using the same number of physical properties for binary particles and drums, rotating at a speed series from 0.01 to 21.9 rad/s. By varying the rotational speed, four flow regimes were produced in the simulation. Flow regimes, velocity vectors, normal forces, and the number of contacts between 1 mm particles and 3 mm particles were comparatively analyzed, especially the particle velocity at transient changing rotational speeds. The results showed that four flow regimes were found at the same rotational speed for three different rotating drums, and normal forces were weakest for the cataracting regime; moreover, the three layers of particles were damaged when the rotational speed was suddenly decreased and the velocity direction of the particle motion was changed at the top of the particles’ bed. The maximum number of contacts was found with the rolling regime, based on the simulation results. The number of contacts of the major axis circular drum was smaller than for the minor axis at the same rotational speed, and the number of contacts of the elliptical drum was the largest among the three rotating drums.