The work is devoted to a horizontal tank composed of cylindrical shell closed with ellipsoidal heads and supported at the ends. The tank is loaded with internal or external pressure. For the first load case, a strength condition was formulated, for the other one -the condition of stability of the structure. An optimization model was formulated, in which the mass of the tank subject to the strength and stability conditions was assumed as an objective function. Optimal proportions of geometric dimensions for a family of the tanks of various capacities provided with heads of various convexities were determined. The results were presented in the form of plots. A function was proposed that approximated the solution and could be useful for purposes of designing of the tanks.