The bolted connections inserting gasket such as circular flange connections have been widely used in mechanical structures, which is nuclear and chemical industry, and so on. They are usually used under internal pressure. And they are required the high sealing performance. In the circular flange with non-asbestos compressed sheet gaskets, the two flange surfaces, raised-face and flat-face, are used. The raised-face flange on the sealing performance is examined by many researchers and reported. The flat-face is well known that flange rotation is smaller than that in raised-face flange under the internal pressure. However the sealing performance of the flat-face flange connection isn't examined. Thus, the sealing performance of the flat-face flange connection is not examined. In this paper, the contact gasket stresses of these connections under internal pressure are analyzed using the finite element method (FEM) of each flange surfaces, taking into account a hysteresis in the stress-displacement curve of the gasket. And then, using the contact gasket stress distributions obtained from FE analysis and the relationship between gasket stress and leak rate obtained from a gasket sealing test (JIS B2490), method for estimating an amount of leakage is examined. The leakage tests were also conducted to measure an amount of gas leakage using an actual circular flange connection with a gasket. The estimated results are in a fairly good agreement with the experimental results.