The invention is directed to carbon fibers having high tensile strength and modulus of elasticity. The invention also provides a method and apparatus for making the carbon fibers. The method comprises advancing a precursor fiber through an oxidation oven wherein the fiber is subjected to controlled stretching in an oxidizing atmosphere in which tension loads are distributed amongst a plurality of passes through the oxidation oven, which permits higher cumulative stretches to be achieved. The method also includes subjecting the fiber to controlled stretching in two or more of the passes that is sufficient to cause the fiber to undergo one or more transitions in each of the two or more passes. The invention is also directed to an oxidation oven having a plurality of cooperating drive rolls in series that can be driven independently of each other so that the amount of stretch applied to the oven in each of the plurality of passes can be independently controlled.