Surface trimming is an essential function in a surface modeler for representing multi-boundary surfaces, blended surfaces, and surfaces with islands or pockets. A procedure and a data structure for designing trimmed surfaces were developed. For generating a trimmed surface, edges (curves difined on a surface) are generated and trimmed first. Then the trimmed edges are selected sequentially to form a closed loop. The data of supporting surface, surface on which the trimmed surface is defined, and bounding edges are stored and used for the application such as NC programming, robot programming, graphic display, etc.