Abstract: Forced longitudinal vibration of a drill string is the most important one in its three kinds of vibration.This paper sets up a general model of forced longitudinal vibration to approximate more closely the real situation.This model is suitable for any drill string assembly.The analysis of all kinds of energy loss leads to the formulas for computing the damping factor of longitudinal vibration of a drill string.On the basis of the characteristics of forced longitudinal vibration,the paper suggests a new concept of generalized state vector,which enables us to describe the vibration of a drill string.The generalized transfer matrix method is used to compute the forced longitudinal vibration,thus eliminating the need of analytical solution.The generalized formulas used for computing the steady-state response of forced longitudinal vibration of any drill string assembly is given,and appropriate ways for computing the state vector under different measurement conditions are proposed.