GLAREs as hybrid materials are widely employed members of fibre metal laminates (FMLs) in aerospace structures. Delamination is one of the most critical failure modes that happen during the manufacturing or service life, decreasing the stability and reliability of the GLARE laminates. Accordingly, this study presents an investigation of the shear buckling phenomenon, a very common load condition in aerospace structures, of different GLAREs, differentiating in the laminate layout, containing embedded delamination by the FEM ABAQUS software. The cohesive zone interface elements of FM94 are considered to evaluate the delamination growth. This parametric study displays the effect of the initial delamination dimension and its position as well as the thickness of the metal layer on the stability of GLARE laminates. The model predicts the stability reduction of GLARE laminates as a function of the delamination radius and its position. The results show that aluminium layer reinforcement increases the overall stiffness and shear buckling capacity and the specimen’s resistance to delamination growth. In addition, the produced results in this study can encourage designers to select appropriate GLARE grades based on the intended application, such as different shear loading conditions and available raw materials.