The paper deals with the dynamic modeling of bio-inspired robots with soft appendages as flying insect-like or swimming fish-like robots. In order to model such soft systems, we here propose to exploit the Mobile Multibody System framework introduced in [1], [2], [3]. In such a framework, the robot is considered as a tree-like structure of rigid bodies whose the joint evolution is governed by stress-strain laws or control torques. Based on the Newton-Euler formulation of these systems, we propose a new algorithm able to compute at each step of a time loop both the net and passive joint accelerations along with the control torques supplied by the motors. For the purpose of illustration, following our works begun in [4], the proposed algorithm is applied to the simulation of the hovering flight of a soft flapping-wing insect-like robot (see the video at [5]).