The functional properties of "TiNi-TiNi" and "TiNi-bronze" bimetallic composites produced by explosion welding were studied. It was found that the bimetallic TiNi-based shape memory composites were able to demonstrate a recoverable strain variation on cooling and heating after preliminary deformation. However, the maximum recoverable strain did not exceed 0.7 %, and this value did not depend on the elastic properties of the elastic layer. It was presented the scheme for the estimation of the recoverable strain that may be observed in the bimetallic shape memory composite, and shown that the maximum recoverable strain was found if the stress generated in the composite on heating of the deformed composite was larger than the flow stress measured in the austenite state (TiNi alloy).