The investigation of thermo-mechanical processes in materials and elements with shape memory effect (SME) and the simulation of dynamics of elements and drives based on alloys with shape memory and taking into account the adaptation properties of material are carried out in order to develop adaptive-controlled thermomechanical drives or actuators, heat regulator and automation tools of technological processes. The effect of the thermal cycling modes and the magnitude of deformation, which induces the shape memory effect, on the level of reversibility of the deformation, the implementation of the effect of reversible shape memory, the magnitude of the excited force, and the recoverable deformation are investigated. A generalized dynamic model of a technical mechanism based on the elements with SME is developed. The model formally describes adaptive control of mechanism, based on which, the adaptation algorithms can be synthesized. The developed models can be used in the calculation and design of various thermomechanical drives and actuators, heat regulators, thermal compensators and damping devices based on elements from shape memory alloys, as well as in a synthesis of adaptive control algorithms of continuous and discrete classes in the terminal control, homing guidance and stabilization modes.