A general-purpose solution scheme of inverse dynamics for link systems called the parallel solution scheme, was developed on the basis of a finite element approach. It can be applied to dynamics compensation of different types of configurations such as open-loop, closed-loop, or multibranch link systems, and can also deal with elastic deformations of constituted links without the need to revise any part of the scheme. The main objective of this study is to extend the use of the scheme to dynamics compensation of underactuated link systems, and to obtain highly stable feedforward control of those systems by feeding the calculated torque. A solution scheme of kinematics with updated transformation algorithm is also developed on the basis of the finite element approach, in order to calculate target motions of the systems including passive joints and flexible links. The feedforward control experiments of several underactuated link systems are carried out, and the validity of the dynamics compensation is confirmed.