This article proposes a general modelling approach for locomotion dynamics of Mobile Multibody Systems (MMS) containing passive internal degrees of freedom (dofs) concentrated into (ideal or not) joints and/or distributed along deformable bodies of the system. The approach embraces the case of non-holonomic mobile multibody systems with passive wheels, the pendular climbers and the locomotion systems bio-inspired by animals that exploit the advantages of soft appendages such as the fish swimming with their caudal fin or the moths using the softness of their flapping wings to improve flight performance. The article proposes a general structured modelling approach of MMS with tree-like structures along with efficient computational algorithms of the resulting equations. The approach is illustrated through non-trivial examples such as the 3D bicycle and a compliant version of the snake-board.