An investigation is carried out to understand the buckling behaviour of local delamination near the surface of fiber reinforced laminated plates under mechanical and thermal loads. The shape of the delaminated region considered is rectangular and triangular. The displacement expression is composed of items with the effect of tension-shear coupling and the effect of bend-torsion coupling. The critical strains of laminated plates with various shaped local delamination and different stacking patterns are obtained by making use of the energy principle. Analytical predictions for delamination buckling loads are shown to correlate well with experimental results for a number of different delamination shapes.