A redundant Lagrangian/finite element approach is proposed to model the dynamics of lightweight spatial manipulators with both flexible links and joints. The links are assumed to be deformable due to bending and torsion. The elastic deformations of each link are expressed in its tangential (clamped free) local floating frame. The constraint equations due to the connectivity of the links are added to the equations of motion of the system by using Lagrange multipliers. The resulting mixed set of nonlinear differential equations and algebraic equations (DAEs) is solved numerically to predict the dynamic behavior of the system. The dynamic model derived here is free from the assumption of a nominal motion and takes into account not only the coupling effects between the rigid body motion and the elastic deformations of the links, but also the interaction between flexible links and actuated flexible joints.