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In this study a higher-order shear deformable, analytical model is developed to analyze composite shells with parametric modeling capabilities. The material and geometric properties and loading conditions can be varied as parameters which satisfy a set of constraints to allow the designer to achieve a sensible and computationally feasible FE model. The formulation is derived with equal emphasis on all the six strain as well as stress components at a generic point in the shell laminate. Unlike many other available models which violates the equilibrium conditions at lamina interfaces, this model satisfies the equilibrium conditions at the lamina interfaces for a certain class (angle-ply and unidirectional orthotropic) of laminates.