Adhesive structures, such as composites, are very common in engineering. Because adhesive structures always fail in the adhesive layer, it is valuable to study refined analysis methods for adhesive structures. In this paper, an adhesive structure is modelled as a three-phase orthotropic structure, and Green's function solution of the elastic field in this three-phase orthotropic structure, which is acted on by a concentrated tangential force, is presented in the form of elementary functions. Based on this solution, four topics are studied. (1) The stress distributions in the adhesive structure are investigated, and the results show that the adhesive layer has a great effect on the shear stress distributions. (2) The relationship between the stress distributions in the adhesive structure and the fibre orientation of the composite is examined, and the results show that a suitable choice of fibre orientation will reduce the peak stress in the adhesive layer. (3) The relationship between the interfacial stress in the adhesive structure and the elastic constants of the adhesive layer are analysed, wherein the analysis shows that different stress components have different sensitivities to the elastic constants. (4) The relationship between the interfacial stresses and the adhesive layer thickness are also studied, and the results show that the interfacial stress will decrease with increasing adhesive layer thickness.