This paper presents a new estimating procedure for sloshing eigen periods of several types of tanks: a liquid cargo tank, a ballast water tank and an anti-rolling tank. There are two steps in the procedure: numerical simulation of the free damping motion of sloshing liquid in a tank, and a time history analysis of free surface elevation of the sloshing liquid. The numerical simulations are executed using the finite difference method (SOLA-SURF scheme). A series of numerical calculations is performed for a half-annul us tank, half-ellipse tanks with and without a baffle plate and a U-tube type antirolling tank. These numerically estimated results are compared with theoretical results derived by the sloshing eigen problems and approximated results using the traditional theory (the U-tube theory). The new procedure is confirmed to be a useful tool for estimating sloshing eigen periods of these three types of tanks.