Many aircraft composite structures experiencing the high operational loads must have the specified mechanical stiffness to prevent some structural failure due to the inadmissible deformations. Usually, such parts are manufactured using composites with orthotropic symmetry, which provides the best combination of structural rigidity, strength, and weight. In this chapter, we consider a cantilevered long tube-like composite structure with varied cross-section that is manufactured by winding of glass fiber unidirectional tape. The operational loads include the bending forces and the distributed torques. To reduce the total strain energy and peak von Mises stress, the search of the best lay-up scheme and its angles is performed. The wall thickness, lay-up scheme, and the total number of layers for each modeled design are assumed as unchanged along the tube, whereas its mechanical properties are considered as homogenized and dependent on the lamina properties and lay-up scheme only. The search of the pseudo-optimal design includes the analysis of all moduli angular distributions for each lay-up stacking. The better solutions are then studied by using the finite element model of the structure for three most critical load scenarios. The choice of the most preferred design is made by discarding the solutions with sharply degraded structural rigidity at least at one load scenario.