The flexible clamp used in linear ultrasonic motors (LUMs) not only supports the motor but also simplifies the structure and improves the vibration characteristics. However, the flexible clamp causes the mechanical drift phenomenon, leading to a reduction in positional accuracy. To solve this problem, the mechanical drift mechanism and the control methods of V-shaped LUMs are investigated in this work. First, a mechanical model of the stator of a LUM with a flexible clamp is established to analyze the reason for the mechanical drift. Then, based on the mechanical model, the rules of the appearance of mechanical drift in clamping components with different stiffnesses and shapes are studied. The results indicate that mechanical drift is obvious when the stiffnesses of the two flexible clamps are different, whereas it hardly occurs when clamping components with tremendous tangential stiffnesses are used. Finally, two new types of V-shaped LUM stators that have a flexible clamp on one side and an analogous straight-beam clamp on the other side are proposed. Experiments were conducted to validate the mechanical model analysis and the clamp drift findings, and the results demonstrate that the novel motors have little mechanical drift and stable running characteristics and can be used in precision motion platforms.