The purpose of the study was to develop a mathematical model of a flat composite spring operating in the region of small displacements and having a shape memory effect. To describe the behavior of the material, we applied a phenomenological approach based on the phase transition diagram; as the material model, we chose the Brinson phenomenological model. As a result, we proposed relationships for determining the reduced mechanical characteristics of a monolayer equivalent to a composite layer in the spring. The memory effect was taken into account by an additional internal force factor, i. e. the shape memory moment during bending, which resulted from the cross-section orientation of the martensite. To obtain the elastic characteristic of the spring, we used a finite element approach, in which the shape memory moment acts as an additional nodal load. Eventually, we introduced an algorithm for the dependence between the bending moment in the section and the shape memory moment for isothermal loading in the martensite stability zone and obtained the dependences of the shape memory moment during bending on the bending moment for various configurations of the cross-section of the spring.