The invention discloses a production method of elastic fibers, including the following process steps: 1) mixing 4 parts of polypropylene, 6 parts of polyethylene, 6 parts of polyolefin, and 85 parts of an allyl elastomer, feeding into a storage bin of a twin screw reactive extrusion machine; 2) passing through ten heating temperature zones in turn for melt mixing extrusion; 3) solidifying into strips through a cooling waterway, dragging and chopping into particles by a pelletizer; 4) drying; 5) screening; 6) feeding into a bin of a screw extruder, extruding the melt material by four different heating temperature zones of the screw extruder; 7) ejecting out the elastic fibers through ejection mouths; 8) side blowing cooling the ejected elastic fibers and passing the ejected elastic fibers through a curing tunnel, lubricating and applying oil through an oil tanker, feeding into a first godet roller, then through a second godet roller; and 9) winding the fibers through a winding machine. The production method enables the fibers to possess the performances of chlorine resistance, ultraviolet radiation resistance, acid and alkali resistance, high temperature resistance, wear resistance, and air permeability, at the same time helps to reduce energy consumption, and has no emission of waste water, waste gas, and waste residue.