The optimum sail geometry is analytically obtained for the case of maximizing the thrust under equality and inequality constraints on the lift and the heeling moment. A single mainsail is assumed to be set close-hauled in uniform wind and upright on the flat sea surface. The governing parameters are the mast height and the gap between the sail foot and the sea surface. The lifting line theory is applied to analyze the aerodynamic forces acting on a sail. The design method consists of the variational principle and a feasibility study. Almost triangular sails are found to be optimum. Their advantages are discussed.