Methods of producing silicon carbide fibers. The method comprises reacting a continuous carbon fiber material and a silicon-containing gas in a reaction chamber at a temperature ranging from approximately 1500° C. to approximately 2000° C. A partial pressure of oxygen in the reaction chamber is maintained at less than approximately 1.01×102 Pascal to produce continuous alpha silicon carbide fibers. Continuous alpha silicon carbide fibers and articles formed from the continuous alpha silicon carbide fibers are also disclosed.