Special two- and three-dimensional adhesive elements have been developed for determining “mechanics of materials” level stresses in adhesively bonded joints. For two- dimensional analysis, the adherends are modeled as simple beam-truss elements connected by special adhesive elements that utilize offset nodes located at the mid-plane of the respective adherends. The technique has been extended to three-dimensional geometries by modeling the adhesive as a single element through the thickness with offset nodes located at the mid-plane of the adherends. The adherends are modeled as conventional plate elements. The simple models permitted by these elements provide good convergence to closed-form solutions for peel and shear stresses in 2-D lap joints. The 3-D elements offer significant computational efficiencies over more widely utilized three-dimensional element formulations. Although the results obtained using these elements are not sufficient to detect singular stress fields, or certain other details, they have proved to be very useful in understanding the overall stress states in bonded structures. Preliminary determination of strain energy release rates using the 2-D elements also appears to be quite promising.