The method for producing a wire element by interlacing at least a first strand and a second strand, during which strand tension control is effected by includes defining an assembly tension set point representative of a state of longitudinal tension to be obtained in the first strand when said first strand reaches the assembly point. The method also includes measuring the actual assembly tension applied in the first strand, said measurement being taken at a first tension measurement point located along the first strand and upstream of the assembly point. The method proceeds with operating a tension regulating member such as a capstan, which acts on the first strand upstream of the assembly point such as to cause the actual assembly tension within said first strand to converge automatically towards the assembly tension set point.