Abstract: In this paper a mathematical model capable of handling a three dimensional flexible n-degree of freedom manipulator having both revolute and prismatic joints is considered. This model is used to study the longitudinal, transversal and torsional vibration characteristics of the robot manipulator and obtain the kinematic and dynamic equations of motion. The presence of prismatic joints makes the mathematical derivation complex. In this paper, for the first time the prismatic joints in addition to revolute joints have been considered in structure of a 3Dflexible n-degree of freedom manipulator. The kinematic and dynamic equations of motion representing longitudinal, transversal and torsional vibration characteristics have been solved inparametric form with no discretization.In this investigation, in order to obtain an analytical solution of the vibrational equations, a novel approach is presented using the perturbation method. Through solving the equations of the motion, it is shown that the mode shapes of the link with prismatic joints can be modeled as the equivalent clamped beam at each time instant.As an example, this method is applied to a three degrees of freedom robot with revolute and prismatic joints. The obtained equations are solved using perturbation method and the results are used to simulate the vibrational behavior of the manipulator.