Core yarns are known as multi-component yarns in which one component, the core material, stays nearly at the center of the yam while the others cover it. Stretch knitted or woven fabrics can be made from core yarns in which the core is an elastomeric filament such as Dorlastan(R), Lycra(R), Glospan(R), etc., and the covering is made from staple fibers. Elastomeric core-spun yarns are usually made on cotton, worsted, or woolen spinning systems. In this study, we briefly describe a method of producing a polyester/viscose covered Lycra core yarn on a modified short-staple ring spinning frame. We also examine the polyester/viscose staple yarn and the polyester/viscose core-spun yarns produced on the modified system. The experiment and test results show that core positioning has a direct effect on the structure, properties, and performance of these core-spun yarns.