Abstract Past dynamic studies of blown‐film extrusion have been confined to the stability analysis of the linearized equations. The full set of nonlinear equations comprises a system of partial differential and algebraic equations with boundary conditions that vary from author to author. In this paper, the Numerical‐Method‐of‐Lines, which combines finite‐difference methods with ordinary differential/algebraic equation integrators, is used to solve the full system. Appropriate boundary conditions are selected to give physical results that compare well with experiment. An important boundary condition is the “minimum order reduction” condition on the gradient of the bubble‐tube radius with respect to distance above the extrusion die (the axial position). Transient startups and operational disturbances are examined. Calculations show the influence of oscillations in operating conditions such as heat transfer or inflation pressure on the bubble‐tube radius and film thickness. Steady‐state results obtained by integrating the transient equations for a sufficiently long time are qualitatively in agreement with experiment, in contrast to past simulations of these equations.