In this work the structural behaviour of the so-called grid-stiffened structures is studied by means of finite element analysis; the focal target is to verify their applicability in the design of a low cost and low weight aircraft fuselages, to fabricate in composite material using the Filament Winding technology. A grid-stiffened structure is characterized by beam elements (ribs) and shell elements (skin); the ribs constitute the main reinforcements and individuate the type of grid structure. Starting from a set of requirements, a lattice structure is sized, that is a grid-stiffened structure with ribs only and without a skin (inner and/or outer). The characteristics of the isotropic material used for the ribs are derived from the properties of a common high-strength graphite/epoxy composite material. The variables to optimise are: number of helical ribs, number of circumferential ribs, winding angle of the helical ribs with respect to the longitudinal axis, rib height, circumferential rib thickness, helical rib thickness, distance between the helical ribs, distance between the circumferential ribs. The design criteria are no-strength failure and no-buckling failure at ultimate load for the beam elements of the ribs. The best lattice structure has all the margins of safety (MS) as positive and the minimum mass. In particular, the margins to check are: beam tension MS, beam compression MS and global buckling MS. Finally, a scaling method for a lattice structure is also developed in order to apply the right loads on a scaled structure for the experimental tests. All the analyses are performed with a general-purpose finite element software (MSC/Nastran).