An illustrative method of making an elevator load bearing member having at least one elongated tension member at least partially covered by a jacket includes mixing a flame retardant with a polymer material. The flame retardant is selected from a group consisting of (i) a halogen-free melamine based intumescent comprising melamine cyanurate, melamine-phosphate, melamine pyrophosphate or melamine polyphosphate in an amount up to about 20% by weight of the thermoplastic polymer or (ii) a filled polymer having a nanoscale filler chemically bonded to a matrix phase. Applying the mixed flame retardant and polymer material to the tension member forms a jacket of a desired shape.