We study the problem of evolution of stresses in composite systems, which contain active elements made of an alloy with shape memory, when such elements are cooled during the interval of the austenite-martensite phase transformation, i.e. during the stage of straight transformation. A similar situation takes place when on the stage which precedes to cooling, the active elements are subjected to heating and produce high reactive stresses under considerable strains (the phenomenon of shape memory). The problem of determination of stresses in compound systems with active elements made from alloys with shape memory is of interest since the stressed state in the contact zone is characterized by significant variability, and the substantial stresses produced at that determine the strength of the system as a whole. These stresses can determine the strength limitations, which should be taken into account when designing optimal controlled composite systems and active composites. Accounting for the heterogeneity of stressed state produced by the shear stresses in the zone of inclusion at transition of strains, generated in active elements and component system, as a whole, sometimes can become substantial, especially when making estimations of strain-force characteristics of structural elements. It should be also noticed that because of peculiarities of the constitutive relationships for study of stress-strain state of elements made from alloys with shape memory, it is desirable to use the approaches based on application of smaller number of auxiliary hypotheses. Any way, application of these or those hypotheses requires additional testing and substantiation.