This paper presents an exact, two-dimensional (2D) quasi-static elastic analysis of predelaminated composite panels subject to arbitrary transverse pressure loads. The piecewise linear spring model and the shear bridging model are, respectively, used to simulate the normal contact and shear frictional behavior between the interfaces of the existing delamination. This general contact model can be further reduced to the “friction-free model” and the “constrained model” by assigning extreme values to the spring stiffnesses. The analysis yields a closed-form solution for the 2D displacement and stress fields. To predict the delamination propagation, different propagation criteria as suggested in the literature are used. Calculated load–displacement responses and delamination threshold loads are in good agreement with existing experimental data. The results are further compared against simple fracture models and a model that uses a modified classical laminated plate theory for the predelaminated composite with fracture criteria, showing an overestimation of the delamination threshold loads. The 2D elasticity theory that is formulated can be used with confidence to study other multilayered structures with multiple delaminations and subject to arbitrary loading profiles.