The Finite Element (FE) method could be able to address the stress analysis of bonded joints. Nevertheless, analyses based on FE models are mainly computationally cost expensive and it would be profitable to develop simplified approaches, enabling extensive parametric studies. Firstly, a one-dimensional 1D-bar and 1D-beam simplified models for the bonded joint stress analysis, assuming a linear elastic adhesive material, are presented. These models derive from an approach, inspired by the FE method using a formulation based on a four-node macro-element, which is able to simulate an entire bonded overlap. Moreover, a linear shear stress variation in the adherend thickness is included in the formulation. Secondly, a numerical procedure is then presented to introduce into both models an elasto-plastic adhesive material behavior, while keeping the previous linear elastic formulation. Finally, assuming an elastic perfectly plastic adhesive material behavior, the results produced by simplified models are compared with the results predicted by FE using 1D-bar, plane stress, and three-dimensional (3D) models. Good agreements are shown.