This study was conducted to investigate dynamic characteristics of agricultural tractor with a particular interest in ride vibrations when it is subjected to various excitation forces. As the first part of it this paper describes development of dynamic model of a tractor-trailer system and its equations of motions. An 3 dimensional 16-degree-of-freedom dynamic model for a tractor-trailer system was developed and its equations of motions were derived, which will be used to investigate the effects of irregular ground surface and excitation forces due to the engine mounted on the tractor. And the excitation forces were also formulated analytically. The transition matrix method and QR algorithm were proposed for numerical solution of the equation of motions fur the developed model. The later parts of the study will include a proof of the model and optimization from which tractors can be designed to minimize the ride vibrations. This will be presented in the second and third papers to be followed shortly.