During the drilling and repairing of wells, the pipe string transfer equipment has a high work frequency. The movement accuracy, response speed, and controllability of the equipment have significant impacts on the stability. In this paper, we propose an analysis method of mechanical arms to lift pipe strings using a rigid–flexible coupling model. With the mechanical arm as a flexible body and the mechanical hand as a rigid body, a numerical calculation model of the rigid-flexible coupling of the system was established based on the Lagrangian equation. ADAMS and Ansys software were applied to numerical simulations of this system to investigate the lifting characteristics, the influence of the operation parameters and structure parameters, and the contact collision analysis of the mechanical arm. The conditions of rigid–flexible modeling for the multi-body system and the main factors affecting the vibration characteristics of the flexible arm are described. We conclude that the arm should be modeled as a rigid body if the structure parameter [w/l] (elastic deformation/length) is between 1/650 and 1/1000, the system can be modeled as a rigid–flexible coupling if [w/l] is between 1/400 and 1/650, and the arm should be modeled as a flexible body and the influence and compensation of the control method should be considered if [w/l] is between 1/250 and 1/400.