Delamination is one of the most common modes of defects of laminated composite shell roofs. A review of literature that exists on composite shells reveals that the research reports on delaminated shells are very few in numbers. Present paper deals with the static analysis of delaminated composite conoidal shells with simply supported boundary condition and subjected to centrally applied point load. For the present study work a finite element approach using eight noded isoparametric shell element with five degrees of freedom per node is employed. A multipoint constraint algorithm is incorporated, to satisfy compatibility of deformation and equilibrium of forces and moments, which leads to unsymmetrical stiffness matrix. This formulation is validated through solutions of benchmark problems. Lamination and extent of delamination area are varied to compare the performances of delaminated conoidal shells against those with no damage. Based on the present comparison some engineering conclusions are also included in this paper, which will serve as future reference.