This paper provides an overview of demountable connections and elements for steel and composite structures. Demountable connections are generally assembled from prefabricated structural members which can be reused after dismantling. This paper investigates innovative connections which enable steel and concrete framed structures to be made demountable. Demountable connections considered in this paper include beam-beam connections, column-column connections and beam-slab connectors. The finite element models for the nonlinear inelastic analysis of coped beams, column-column connections and composite beams are developed based on nonlinear finite element analysis techniques using the commercial finite element program, ABAQUS. The behaviours for coped steel beams and composite beams are then compared with the corresponding experimental results. The finite element models are used to investigate the effects of material and geometric properties on the behaviour of demountable connections. The finite element models can efficiently predict the plastic damage in the coped steel beam used in beam-beam connections. It is demonstrated that the coped beam can be made demountable up to a load of about 50% of the ultimate load which is greater than typical service loads. The computational results indicate that increasing the sleeve length and reinforcement ratio increases the stiffness and ultimate tensile strength of demountable column-column connections.