The design of a spread mooring system of given pattern with single segment lines on a flat seafloor is formulated as a mathematical programming (optimization) problem. Design variables are the outboard length and initial tension in each line. Constraints limit maximum tension, anchor pull and anchor uplift for each line under each loading condition. Maximum vessel excursion is limited to a circle of specified radius. The optimal design is that which minimizes total weight of outboard line and is obtained by computer solution of the optimization problem. Three examples are presented to demonstrate the method.