The paper is concerned with a comparative study of both the along and cross-wind responses of a tall industrial chimney with and without flexibility of soil. The along-wind response has been estimated by means of approaches presented in three Standards: the Polish, the ISO and the Eurocode and by random vibration approach which is outlined below. The cross-wind response has been estimated by means of the three models developed by Vickery and Basu, Ruscheweyh and Flaga and methods presented in Standards: the Polish, the ISO and the Eurocode (Approach 1 and 2). Computer programmes were developed to obtain estimates of responses of a six-flue, 250 m-tall chimney. The analytical results computed according to the methods presented in different standards and random vibration approaches have been compared. Some unexpected conclusions have been observed.