A new exact linear elasticity 2D local model of static bending of a sandwich strip is proposed in the paper. A passage from the strip solution to its counterpart for the sandwich beam is outlined. The model has been obtained by applying the semi-inverse technique as well as some original assumptions imposed on the stress and displacement fields and by expanding functions into a series which is not the Fourier series. New exact linear elasticity boundary conditions for the core at edges of the strip and some realistic edge boundary conditions for the facings have been included in the model. All through-the-thickness boundary and continuity conditions for the structure have been satisfied. Some numerical results are presented and compared with corresponding results predicted by a classical approximate model and by a refined model including the core compressibility.