Abstract: This paper studies the sloshing characteristics of liquid in axisymmetric tanks along the vertical axis at gravity environment. First, the wave equation describing the potential velocity of liquid is established in cylindribal co-ordinates and the analytical solution of linearizing potential velocity of liquid is deduced by means of the separated variable method. Then, the unknown integral coefficients of the solution are determined by collocation method on boundary and the frequency equation is obtained. The frequency para-meters can be numerically given by means of computer. The method has the property of good generality, less calculating amount and higher accuracy compared with other methods. Finally, as examples, numerical results of spherical and ellipticl tanks are given.

Key words: tank, axisymmetry, liquid sloshing, exact solution, collocation method on bound-ary