The critical buckling of composite plates with through-the-length delaminations is studied using exact stiffness analysis and the Wittrick-Williams algorithm. Computational efficiency is achieved by avoiding discretisation into elements, making the method suitable for preliminary aircraft design. Numerical results for longitudinal, transverse and shear loading show a transition from global to local buckling modes as the delamination width is increased. The critical buckling strength is dramatically reduced as the delamination is moved towards the plate surface, but is relatively insensitive to its widthwise location or to the edge conditions. The results are compared with finite element analysis.