A comprehensive analysis of Pollaczek's integral is presented in this paper. It reveals the difficulties found when attempting its numerical solution. This analysis further provides a strategy to avoid these difficulties. A numerical algorithm is then proposed and implemented. Solutions to Pollaczek's integral are provided in graphic form for a broad range of applications. Normalized earth impedances also are provided for underground cables within the same broad application range. Finally, the normalized impedances are compared against those from a widely used approximation.