Recently, in proportion to the increase of earthquake occurrence-frequency and its strength in the countries within the circum-pan Pacific earthquake belt, a concept of earthquake-proof design for huge structures containing liquid has been growing up. This study deals with the refinement of classical numerical approaches for the free vibration analysis of separated structure and liquid motions. According to the liquid-structure interaction, LNG-storage tanks exhibit two distinguished eigenmodes, the sloshing mode and the bulging mode. For the sloshing -mode analysis, we refine the classical rigid-tank model by reflecting the container flexibility. While, for the bulging-mode analysis, we refine the classical uncoupled structural vibration system by taking the liquid free-surface fluctuation into consideration. We first construct the refined dynamic models for both problems, and present the refined numerical procedures. Furthermore, in order for the efficient treatment of large-scale matrices, we employ the Lanczos iteration scheme and the frontal-solver for our test FEM program. With the developed program we carry out numerical experiments illustrating the theoretical results.