► We measured the elongation of a loaded Kevlar-49 fiber at 4.2K. ► We kept a fiber under a constant tension for 8months. ► We obtained an upper limit of 0.028% in the relative elongation. ► The results shows that Kevlar-49 can be used in cryogenic applications. We have measured the rate of elongation of a loaded Kevlar-49 fiber as a function of time at 4.2K. The result puts a worst case upper limit of 0.028% in the elongation rate ΔL/L for a 0.5mm diameter fiber kept under a constant tension of 2.7kg for 8months. A value that is probably closer to reality is actually 0.004%. This result proves that Kevlar-49 can be safely used in cryogenic applications in which high mechanical stability under stress is required.