In the present paper, the shear buckling analyses of adhesively bonded plates including an orthotropic material were performed. The adherends were selected as isotropic homogenous materials and a single adhesive was used in the overlap region. In the adhesive layer, an orthotropic material was located as an inclusion and its shape was assumed with an elliptical geometry. Three different orthotropic inclusions were selected: glass/epoxy, graphite/epoxy, and boron/epoxy. The effects of the inclusion shape and properties on the shear buckling were investigated via finite element analyses. The finite element analyses were verified according to an analytical solution having a full homogeneous isotropic adhesive layer. The analysis results showed that the maximum buckling loads were obtained when using the boron/epoxy inclusion compared to the glass/epoxy and graphite/epoxy inclusions. In addition, the possibility of delamination in the vicinity of the inclusion was examined. By this means, the influences of the delamination shape and magnitude on the critical buckling load were investigated. The greatest effect was obtained when the delamination shape was close to a circle and its magnitude was the largest.