A new approach for a composite road optimum design is suggested. The road is subjected to uniaxial loading. A structure of the road is a core consisting of unidirectional fibers and a pair of spirally-cross plies. The core is considered as transversally-isotropic solid body and the pair of spirally-cross plies is considered as thin orthotropic shell. Design variables are a normalized thickness and a reinforced angle of the pair of spirally-cross plies. Minimum of the road cross-section area is used as the optimum criterion. Criteria of maximum stresses and strains are used as the strength constraints for the road core and a quadratic criterion of ply strength with different compression and tension strength is used as the strength constraint for the pair of spirally-cross plies. The problem is reduced to an unconstrained minimization problem. The solution method is the method of descent. The optimal structure is obtained for a simply supported carbon rod subjected to uniaxial compression.