The truss element, due to its simplicity, can fulfill the need to model multibody systems in a way that reduces the size of the problems or improves the efficiency of calculations. The truss element can be used to model rigid and flexible bodies as well as several joints with a single truss element or with aggregates built up from a number of truss elements. With an extended mass description, planar binary rigid links or links that can undergo a uniform dilatation with pin joints can be modelled by a single truss element. Planar ternary elements can likewise be modelled by three truss elements. In three dimensions, a rigid body can be modelled by six truss elements along the edges of a tetrahedron, but also three truss elements can be combined to form a triangular membrane element or six truss elements to form a constant-strain finite solid element. Applications to two benchmark problems and a Delta robot are given.