This study develops an analytic method for potential flow problem of liquid in rigid tank boundary during earthquake. Boundary surfaces wrapping the liquid volume are discretized and boundary integral equation is re-formulated in matrix form via Boundary Element Method (BEM). Boundary conditions in each surface are expressed in linear simultaneous equations by time marching procedure. Verifications and accuracy tests of BEM and time marching scheme are performed and some numerical examples of transient responses are given. One of the main purposes of the study is to construct an analytic model for liquid-structure interaction problem and liquid-soil-structure interaction problem. For this purpose, every procedure of numerical implementation of boundary elements is formulated and performed taking account of combination with isoparametric finite shell elements. Actually, the implementation of interaction alalyses is out of this scope, therefore developed method is only applicable to thick-walled tank with such assumption that the deformation of tank wall and base is negligible.