Cylindrical wire or fiber electrodes are attractive for electro-analytical applications, but the theory of transient methods at such electrodes is complicated, implying that theoretical discussions and experimental data analysis usually rely on various approximations. In particular, a number of approximate expressions has been proposed in the literature to describe the chronoamperometric limiting current at such electrodes. All these expressions have a low accuracy. In the present work a new, highly accurate and computationally inexpensive procedure for computing the current is presented. The procedure relies on local polynomial approximations covering the entire time domain, and provides at least 14-15 significant digits. It can therefore be useful both for theoretical purposes (e.g. as a source of reference values for testing electrochemical digital simulation techniques that are usually less accurate), and for the analysis of the experimental data. (C) 2011 Elsevier Ltd. All rights reserved.