Boil off rate (BOR) of cargo is defined as the value at a fully loaded condition of liquefied gas, being 0.1 to 0.25% of total volume per day for conventional LNG carriers. Half of the ships life is, however, ballast condition and a partial loading is also required according to circumstances. In these conditions, since the temperature distributes between cargo temperature and comparatively high temperature inside the tank, method of BOR calculation is not established yet. Heat gain to the cargo should include the radiation heat from the tank wall of vapor space and conduction heat along the tank wall as well as the heat gain through the insulation over the wetted areas, this means the temperature distribution along the tank height from the cargo level should be verified for an accurate estimation of BOR. In this paper author analyzed the temperature distribution of tank wall and vapor taking the heat radiation from tank wall to liquid by using an approximate method and the convection heat between tank wall and cargo vapor into account, accordingly conduction heat through tank wall, radiation heat and cargo boil off were calculated at various cargo levels. Since the analytical solutions of spherical shell are not practical, author adopted the Picard's method as an initial value problem and numerical solutions were obtained. For the rectangular tank such as membrane tank and LPG tank analytical solutions were obtained. As the results of calculation it was found that LNG BOR of membrane tank is as much as several times greater than that of spherical tank especially at the very low cargo level due to the greater radiation heat emitted from the comparatively greater dried area of tank wall and LPG, BOR is governed by the heat gain through the insulation of wetted areas.