A composite elastic filament with a rough surface, composed of a sheath component comprising a fiber-forming thermopastic polymer such as polyamide, polyester or polyolefin and a core component comprising a fiber-forming elastomer such as polyurethane or polyester elastomer, wherein the core to sheath compositing ratio ranges from 1/1 to 100/1 in terms of the cross-sectional ratio and the core part has a smooth periphery uniformly extending in the direction of the fiber axis while the sheath part covering the core part has a rough surface wherein numerous ribs are formed in the circumferential direction in proximity to the fiber axis. It can be readily produced by the melt composite spinning of the core and sheath components at the above-specified compositing ratio, followed by stretching 1.1- to 10.0-fold and relaxation. The filament has excellent elastic properties, a small surface friction coefficient and a matting effect due to diffuse reflection of light caused by the rough surface, and is agreeable when worn in the form of a fibrous structure, particularly as lady's stockings.