The layout of fiber composite structures compared to that of structures made from conventional homogenous isotropic materials is far more difficult, because a fiber composite (laminate) is built up of several unidirectional layers (UD-layers) with fibers set at different angles. A contribution to the structural analysis and preliminary design of a fiber-reinforced conical shell is made in this paper. The equations of the membrane theory are used for analyzing the shell behavior. The design, with the objective of obtaining minimal deformation at minimal weight, subject to a set of failure constraints, is achieved by formulating and solving a compromise Decision Support Problem. Some designs of a fiber reinforced conical shell subjected to pressure load and temperature are presented.