An elastic longitudinal net (1) for longitudinal food products, especially cold meat products, is formed as a sleeve having at least one longitudinal main warp (21) of a tightening chain weave having at least one substantially inextensible thread (213, 214), and at least one weft (3) having at least one elastic fiber and circumferential sections (31), the ends of which are interweaved substantially perpendicularly between the substantially inextensible fiber and longitudinal sections (32) existing between neighboring circumferential sections (31) and running in a concurrent manner relative to and weaved with at least one main warp (21). The longitudinal sections are interweaved through at least one main warp (21) substantially perpendicularly relative to its longitudinal axis, passing through loops (215, 216) of the at least one substantially inextensible thread (213, 214) of the main warp, forming a serpentine run having at least two external loops (321).