An analytical model was developed to study a mixed adhesive single-lap joint and a mixed adhesive double-lap joint to perform from low to high temperatures. A high temperature adhesive can probably be used alone, however it is brittle at low temperatures. On the other hand, a low temperature adhesive cannot be used alone at high temperatures since it is too flexible to support the applied load. To overcome this problem, one possibility is to use a mixed adhesive joint, which consists of a high temperature adhesive in the middle of the overlap and a low temperature adhesive at the ends of the overlap. After an extensive literature review on the existing analytical models for both single- and double-lap joints, it was concluded that the Frostig et al.'s model was easy to partition for the inclusion of more than one adhesive and could include geometric features such as the adhesive spew-fillet. First, this analytical solution was extended to account for the shear deformation in the adherends and the nonlinear geometric effect characteristic of single- lap joints. Then, it was further developed to model mixed adhesive joints. The accuracy of this analytical model was assessed by comparison with a finite element analysis. It was observed that both analyses were in very close agreement. A parametric study of various joint parameters on the stress distribution of mixed adhesive joints is presented in an accompanying paper (Part II). (C) Koninklijke Brill NV, Leiden, 2009