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A review of literature reveals that although singly curved conical shells applicable in many fields of mechanical engineering have been studied by many researchers but doubly curved conoidal shells which are very popular as civil engineering roofing units have not received due attention. Hence relative performances of composite conoidal shells in terms of displacements and stress resultants are studied in this paper under static and dynamic loadings. Free vibration frequencies are also reported. A curved quadratic isoparametric eight noded element is used to model the shell surface. Clamped and simply supported boundary conditions are considered. Results obtained from the present study are compared with established ones to check the correctness of the present approach. A number of additional problems of composite conoidal shells are solved for eight different stacking sequences of graphite-epoxy composite for each of the edge conditions. Uniformly distributed load for static bending analysis and step load of infinite duration for solution of forced vibration problem are considered. The results are interpreted from practical application standpoints and findings that are important for a designer to note, before he decides on the shell combination he will finally adopt among a number of possible options, are highlighted.