The contribution deals with the stress-strain and displacement states in an annulus made of shape memory material and in a shaft made of an ordinary, material after putting them together as a shrink fit. First, in the martensitic state an annulus is loaded and unloaded, so that the inner radius is greater than in the high temperature austenitic state and thus the annulus can be put on the shaft. During heating and from the temperature As onward, the annulus starts shrinking rapidly so that the annulus and the shaft make a shrink fit, In both elements large stresses and corresponding strains are generated. These can be determined by making some assumptions and with the introduction of an effective stress, using uniaxial Stalmans-Delaey-Van Humbeeck's theory of the generation of recovery stresses.