Structural strength and leakage failures are two types of main failures of the bolted flanged connection with octagonal gasket, and they are related to the gasket contact stress and gasket effective contact width to a great extent. The deformation behavior of connection subjected to various bolt loads and medium pressures is studied by numerical simulation. The distribution of the gasket actual contact stress, the change of the gasket average contact stress and gasket effective contact width are discussed. The relationship among the gasket average contact stress, the gasket effective contact width, bolt load and medium pressure are obtained. A model for predicting the leakage rate of the sealing connection with octagonal gasket is developed. Research indicates that the gasket actual contact stress distributes non-uniformly, and at gasket outer flank it is much larger than that at gasket inner flank. Both the gasket average contact stress and the gasket effective contact width increase with increasing bolt load and medium pressure. The leakage rate is largely related to working conditions, gasket contact stress, gasket effective contact area, and so on. The leakage rate decreases with increasing gasket effective contact area and gasket average contact stress, and it increases linearly with increasing medium pressure. The leakage through the octagonal gasket connection shows the characteristic of the laminar flow of incompressible viscous fluid.