Motivated by recent developments in the field of intelligent structures and materials, the present work reports results from an investigation on the dynamical behavior of mechanical systems containing elements with shape memory. Initially, three phenomenologieal theories that attempt to describe shape memory and pseudoelastic effects in metallic alloys that undergo thermoelastic martensitic transfomations are reviewed. Two of these theories are used to model and helical spring. The dynamic response of an oscillator with shape memory spring is investigated. It is shown tlm the system may behave chaotically under certain conditions. A method based on the Finite Element techinique, which can be applied to model the non-linear static and dynamic behavior of adaptive trusses with shape memory elements is also presented. Results of numerical simulations illustrate the complex behavior of these structures.