A woven sailcloth has groups of load-bearing yarns which extend in straight lines through tunnels without being woven. The tunnels are bordered front and back by woven layers and at the sides by crossing-over yarns. Because the load-bearing yarns extend along the tunnels there is no crimp in their longitudinal direction. The load-bearing yarns may include components for resistance to displacement along the tunnels, such as resin adhesives or wrapped-around filament.