Voltage Stability Index (VSI) is a commonly used performance indicator for electrical distribution networks. A high value of VSI at each node implies an overall stable distribution network. A variety of methods are available in literature to determine VSI of a distribution network connected in radial configuration. However, very little has been done to determine VSI for loop-connected distribution networks. This work uses circuit analysis approach to find an expression of VSI for the loop configuration. The derived expression is then used to analyze a section of Korean distribution network. Changes observed in VSI in the presence of line-to-ground faults have also been discussed.