A mathematical model is presented for the charging-up process in an air-entrapped pipeline with moving boundary conditions. A coordinate transformation technique is employed to reduce fluid motion in time-dependent domains to ones in time-independent domains. The nonlinear hyperbolic partial differential equations governing the unsteady motion of fluid combined with an equation for transient shear stress between the pipe wall and the flowing fluid are solved by the method of lines. Results show that ignoring elastic effects overestimates the maximum pressure and underestimates the maximum front velocity of filling fluid. The peak pressure of the entrapped air is sensitive to the length of the initial entrapped air pocket.