Horizontal drilling technology is a widely applied well drilling technology due to its capability of reducing drilling time and cost, and at same time increasing the production. In practice, oil and gas production companies employ rotary steerable system or positive displacement motor to steer the drill bit to follow a pre-planned well trajectory along a desired direction. Therefore, the efficiency and accuracy are the main concerns for the improvement of horizontal drilling technology and drill string vibration is the factor to influence these two major concerns. This thesis illustrates a dynamic mathematical model for the vibration of the bottom hole assembly (BHA) which is an important part of drill string. The mathematical model considers the friction between the wellbore and the BHA and the effect of drilling fluid. It investigates the major influencing factors on the vibration, such as weight on bit, friction coefficient, viscous damping coefficient, and the number of stabilizers. The dynamic mathematical model is validated by the finite element simulation and analysis. Moreover, it can monitor the deformation of BHA real time and help drillers adjusting the parameters when the well path deviates from the original planned trajectory.