This paper presents a method that finds the expected values of self-and mutual impedances of overhead lines with the uncertainties such as the ground resistivity, conductor characteristics, and transmission line structures. For this purpose, this study designs a stochastic random sampling method that removes the uncertainties. A finite element analysis method that includes a single logarithmic closed-form solution to Carson's improper integral is adopted. The impact of an increase in sags and an imbalance in phase conductors on self-and mutual impedances is examined. As a result, the expected values of the selfand mutual impedances of an overhead line are evaluated. It is also shown that as the sag ratio increases, the self-and mutual impedances decrease.