The purpose of this study is to develop a simple one-dimensional model to analyze axially loaded beam-plates containing cracks which extend through the thickness of the beam-plates. Although the material analyzed is isotropic, these cracks will be referred to as delaminations. Buckling, postbuckling, and growth of delaminations in these beam-plates will be analyzed. A finite element method in which all of the terms of the stiffness matrices are obtained by exact integration is employed to determine the linear buckling load and postbuckling solution. The energy release rate is then determined using the postbuckling solution. Curves are provided to show the effect of delamination length and location on buckling loads, energy release rates, and strengths of the beam-plates. The problem of buckling and postbuckling of beams with multiple delaminations is also considered. A method of calculating the energy release rate for beams with multiple delaminations using numerical differentiation is introduced.