In recent years, robots based on fixed base cannot meet the increasingly prominent application needs such as in service and industry. Compared with traditional robots, the mobile flexible manipulator has wider workspace and more flexible characteristics. Therefore, it is gradually becoming the focus of attention. In this paper, the dynamic modeling, analysis and experimental research are investigated by employed MS-DT-TMM (Discrete Time Transfer Matrix Method for Multibody System) for a wheeled mobile robot system with a flexible manipulator. Firstly, the discrete-time transfer matrix method and its solution process are overviewed. Then, the 3-joint flexible manipulator mounted on the wheeled mobile robot is divided into 8 components. According to the idea of modeling method, the system dynamic model is integrated by using the transfer matrix equations of 8 components. Moreover, based on the existing experimental conditions, the dynamic simulation and experimental research of single degree of freedom planar flexible manipulator are carried out. The data results validate the correctness and feasibility of the proposed model. Finally, the numerical simulation research of whole mobile flexible robot is completed. The effectiveness of the model is verified by analyzing the data of wheel forces, links and joints motion, the displacements of the end effector and so on. Further, the comparison of the end errors of the mobile robot carrying rigid link and flexible link in the simulation results demonstrates the necessity of modeling the flexible component in the system.