In engineering practices, the mechanics models of tall chimneys are usually
simplified to discrete systems, and calculated with approximate methods and empirical
formulas, thus inevitably yielding some errors. In this paper, the mechanics model for
continuous systems is adopted and the second Ritz method is employed to calculate the free
vibration characteristics of chimneys. As a result, the natural frequencies of the fore three
orders (i. e., the first, the second and the third orders) and the vibrationmodes of chimneys
are obtained with more precision. In case of aseismic design and seismic response analysis for
chimneys with different heights, using the eigenvalues obtained in this paper to make
calculation is more accurate and simple.