Fundamental period is an important dynamic property necessary for use in SEAOC code, Rumman’s and Indian code procedures for the design of concrete chimneys subjected to earthquake effects. At present two formulae given by A CI Committee 307 and Indian code IS 1893-1983 are preferred most for computing the period. It is found that there is discrepancy in the prediction of these two equations which makes it necessary to examine the problem further. In this paper two rational methods based on Rayleigh’s minimum principal and computer analysis are presented for evaluating the period. Finaily based on computer solution two equations are proposed for reckon- Ing the period expeditlously in the design office.