Stretch-denim is a unique, trendy, and sturdy fabric produced with coarser cotton yarns requiring high consumption of cotton fiber. With the increasing expenses of cotton and the adverse ecological effects linked to its cultivation, it became necessary to investigate an alternative fiber. Jute, despite being a low-cost, biodegradable and sustainable natural cellulosic fiber, is often underappreciated in the textile industry primarily because of its inherent stiffness and poor aesthetics. Herein, a groundbreaking jute/elastane core-spun yarn was produced, for the very first time, to develop fabrics like denim with comfortable stretch. To accurately predict the elastane draw ratio, an I-optimal design, which is a part of the response surface methodology, was employed using design expert software. The study involved nine experimental runs to produce 276 tex core-spun yarns at different elastane draw ratios ranging from 1.4 to 4.6. Surface response models were developed and found statistically significant for mass variation, imperfection, hairiness, tenacity, and elongation of yarn, with p-values below 0.05. Using the optimized formulation obtained from the response models, the optimum elastane draw ratio was determined to be 3.42, which was then used to produce optimized core-spun yarn. The quality parameters of produced yarn closely matched the predicted values, suggesting the effectiveness of the response model in navigating and predicting the characteristics of jute core-spun yarn. The newly developed elastic jute yarn is expected to widen the applications of cellulosic jute yarns where elasticity is necessary, especially in stretch-textile like denim products by replacing the cotton counterpart.