This research determines the traits of bundle twists that appeared on the bundle surface, while the input fiber fleece is transformed to a bundle by using friction drums. A mathematical model is suggested to describe the twists generated in the friction area. Based on the bundle thickness dynamics, which is supposed to determine the geometrical array of the fibers joined layer by layer on the outer surface of an in-process bundle that rotates about the bundle axis, twists on the bundle surface are mathematically described, taking into account the bundle-drum slippage ratio, fiber fleece-feeding angle, and friction ratio. Twists are expressed in terms of the number of twists per length and the twist angle. Results show that the slippage ratio has a significant influence on the number of twists per length, but its influence on the twist angle is minimal. The fleece-feeding angle appears to be an important factor in deciding the twists. In addition, a critical fleece-feeding angle that corresponds to an angle that changes the twist direction could be determined. The friction ratio is positively related to the bundle twists, i.e., the twist number increases linearly with increasing friction ratio. However, the friction ratio is negatively related to the twist angle, i.e., at low friction ratios, the twist angle changed significantly, whereas a high friction ratio led to an almost constant twist angle.