In order to analyze the tracking performance and design the controllers for TMT-M3 control system in the design stage. This paper presents the development of the analytical model of the gear driven large telescope using the lumped mass modeling method. The analytical model includes the telescope structure, its drives, the velocity loop and position loop. First, the modal model of a flexible structure is analyzed based on the finite-element data. And the modal model is transferred into the state-space model, in continuous-time. Next, the drive model is derived, and combined into the velocity loop and position loop. Finally, the impact of the error sources on the control loop properties is simulated. According to the simulation accuracy of the analytical modeling, the analytical model can be used in implementation, such as the model-based controllers.