This paper describes the development of the CCAT telescope finite element model (FEM) and the analyses performed to support the preliminary design work. CCAT will be a 25 m diameter telescope operating in the 0.2 to 2 mm wavelength range. It will be located at an elevation of 5600 m on Cerro Chajnantor in Northern Chile, near ALMA. The telescope will be equipped with wide-field cameras and spectrometers mounted at the two Nasmyth foci. The telescope will be inside an enclosure to protect it from wind buffeting, direct solar heating, and bad weather. The main structures of the telescope include a steel Mount and a carbon-fiber-reinforced-plastic (CFRP) primary truss. The finite element model developed in this study was used to perform modal, frequency response, seismic response spectrum, stress, and deflection analyses of telescope. Modal analyses of telescope were performed to compute the structure natural frequencies and mode shapes and to obtain reduced order modal output at selected locations in the telescope structure to support the design of the Mount control system. Modal frequency response analyses were also performed to compute transfer functions at these selected locations. Seismic response spectrum analyses of the telescope subject to the Maximum Likely Earthquake were performed to compute peak accelerations and seismic demand stresses. Stress analyses were performed for gravity load to obtain gravity demand stresses. Deflection analyses for gravity load, thermal load, and differential elevation drive torque were performed so that the CCAT Observatory can verify that the structures meet the stringent telescope surface and pointing error requirements.