The aim of our contribution is to present the methodology of the optimal design of the supporting part of the landing gear of an ultralight aircraft. The part of the structure in question is built as a composite structure, the properties of which must be appropriately designed using mathematical methods. The main intention is to obtain information about stiffness, deformations and mechanical stresses with respect to core thickness and outer surface. The final goal of the computational analyzes will be the mass minimization of the structure considering the constant stiffness and strength of the object.