Recently in the design of super tankers or LNG carriers which transport a large amount of liquid in the cargo holds, the structural damage due to liquid sloshing becomes an important problem. The impact pressure from sloshing is most violent when the liquid motion of a partially filled tank is in resonance with the motion of a ship. In this paper the sloshing natural periods in liquid cargo tanks are estimated for partially filled tanks with various geometries. Especially the sloshing periods of baffled tanks which are often installed to reduce liquid motion and sloshing forces are calculated. A variational method is adopted to analyze the baffled tank of arbitrary filling depth of liquid. In this approach the liquid domain is divided into several subdomains in which the analytic solutions are potential energy are calculated from the velocity potentials in eachsubdomain. By minimizing the Hamilton's functional, the sloshing natural periods are estimated and the results are compared with experimental and numerical results.