We propose a numerical method for solution of a coupled problem for an elastic carrier in a coupling box made of an alloy with shape memory. The method is based on the new constitutive equations. The effect of reaction of straight martensite transformation on the material volume and the dependence of modulus of elasticity on the material phase content is taken into account. A stress-strain state of a coupling box made of nikeline titanium is examined. It is clarified that the solution of the coupled problem gives us an underestimated value of expanding as compared with the uncoupled one. Consequently, the change of volume and the variation in modulus of elasticity can be neglected.