An analysis of the laminar squeezing flow of an incompressible Newtonian fluid between parallel circular plates containing a single central air bubble in the inertial flow regime is presented in which a successive approximation technique is used to account for fluid inertia effects. A non-linear differential equation for the bubble radius is obtained and is solved by the Runge-Kutta Gill method and then the squeeze film force is determined. Approximate analytical solutions based on the perturbation method for a small amplitude of sinusoidal motion are derived for the air bubble radius and squeeze film force and are compared with numerical results. The combined effects of air bubble and fluid film inertia on the squeeze film force are investigated. The results by the present theory are compared with those obtained using modified lubrication theory. The inertia corrections in the maximum squeeze film force are analysed compared for both the methods for various values of the parameters that influence the motion. (C) 2000 The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.An analysis of the laminar squeezing flow of an incompressible Newtonian fluid between parallel circular plates containing a single central air bubble in the inertial flow regime is presented in which a successive approximation technique is used to account for fluid inertia effects. A non-linear differential equation for the bubble radius is obtained and is solved by the Runge-Kutta Gill method and then the squeeze film force is determined. Approximate analytical solutions based on the perturbation method for a small amplitude of sinusoidal motion are derived for the air bubble radius and squeeze film force and are compared with numerical results. The combined effects of air bubble and fluid film inertia on the squeeze film force are investigated. The results by the present theory are compared with those obtained using modified lubrication theory. The inertia corrections in the maximum squeeze film force are analyzed compared for both the methods for various values of the parameters that influence the motion.