In the framework of the R&D programme for the LHC superconducting magnets, a series of dipole prototypes, manufactered by European firms, will be placed in a test cell of the LHC machine to be tested in the second part of 1992. The design of the cross-section of the full length dipole prototype is a natural evolution from the solutions adopted in the CERN models and prototypes developed and built so far. A detailed finite-element stress and strain analysis was carried out and the results were used to complete the design of the prototype. The optimization of the design was done by studying the magnet behaviour at room temperature, and at 1.8 K in both energized and non-energized conditions. The Lorentz body forces distribution, corresponding to a 10 tesla central field, was computed from a magnetic field analysis by means of the same finite-element package used in the stress-strain analysis. The present paper reports on the main results obtained, and illustrates the guide-lines which were followed in optimizing the design of the cross section.