Computation of the internal impedance per unit length of solid and tubular cylindrical conductors, energized by time-harmonic current, needs to take into account the skin effect. Computation algorithm often involves direct numerical manipulations with Bessel functions, which yields unstable and often erroneous results for large magnitudes of the function argument at high frequencies. In order to alleviate the afore mentioned problem, this paper presents a novel computational algorithm based on the Hankel asymptotic approximations of the Bessel functions for large magnitudes of the arguments. Proposed approximate formulas assure numerical stability and very high accuracy of the numerical solution, even in case of very large function arguments. They are, at the same time, very convenient for the numerical implementation in any high level programming language.