An improved axisymmetric deflected mode analytical model of the adhesive joint of two cylindrical tubes is proposed. An important difference from classical mathematical models is that a more accurate deflected mode model of the adhesive layer is used. The paper is based on the hypothesis that the adhesive layer acts on shear and cleavage. It is also assumed that tangential stress values vary linearly over the thickness of the adhesive layer. To describe the normal stress values in the adhesive layer, the two-parameter Vlasov-Pasternak elastic base model is used. The proposed approach makes it possible to satisfy the boundary conditions at the load-free butt of the adhesive layer and to describe its deflected mode with high accuracy. The problem is reduced to a system of linear differential equations of the fourth order relative to displacements. The solution of the problem is obtained in an analytical form. The model problem is solved.