Abstract: A method for producing copper alloy materials for molds for continuous steel casting and molds as produced by the method. The molds are highly resistant to thermal fatigue and are hardly cracked. To produce the materials, cast ingots of a copper-based chromium-zirconium alloy comprising from 0.2 to 1.5% by weight of Cr and from 0.02 to 0.2% by weight of Zr are heated at between 900.degree. C. and 1000.degree. C. for 30 minutes or longer and then rolled, while hot, at a reduction ratio of 60% or more to be at 850.degree. C. or higher at which the hot rolling is finished , and immediately after the hot rolling, these are rapidly cooled to 400.degree. C. or lower at a cooling rate of 10.degree.C./sec or more, and then aged at between 400.degree. C. and 520.degree. C. for from 1 hour to 5 hours.