A general finite element formulation with the eight-noded isoparametric curved quadratic element applicable for the analysis of doubly curved laminated composite shell structures has been reported in another paper. The bending behaviour of composite shells having the form of paraboloid of revolution has been investigated. In the present paper the finite element formulation is extended to analyse the conoidal shells. Numerical results are obtained for two isotropic conoidal shell problems and one laminated composite shell problem with eight different ply lay-ups and layers. The authors' results of the two isotropic problems compare well with those available in published literature. The numerical results of deflection and stress resultants of eight different types of the third problem are discussed in order to estimate their relative performance for the uniformly distributed loading. The authors further propose a comparative performance matrix to study the relative performance of two laminated composite materials which will be of great help in design.