Cable elasticity can significantly impact the accuracy of Cable-Driven Parallel Robots (CDPRs). However, it’s frequently disregarded as negligible in CDPR simulations and designs. In this paper, we propose a numerical approach, referred to as SEECR, which is designed to estimate the behavior of a CDPR featuring elastic cables while ensuring the Static Equilibrium (SE) of the Moving-Platform (MP). By modeling the cables as elastic springs, the proposed approach correctly predicts which cables become slack, estimates the tension distribution among cables and computes unwanted MP motions, allowing to predict the impact of design choices. The results have been validated experimentally on two cable types and configurations.