Pipes are under the trial of internal and external pressure of fluid in oil well drilling and production. Changes of internal and external pressure of fluid may affect equivalent axis force using for stability analysis of pipes in some cases. Errors in traditional mechanical model and fictitious force are discussed. Mechanical model representing true tubular conditions is established. Internal and external pressure of fluid and its changes have no effects on the stability of hanging pipes. Changes in internal and external pressure of fluid show effects on equivalent axis force and stability of pipes fixed at two ends. Equations for calculating equivalent axis force are established depending on constant axis strain. For pipes fixed at two ends, equivalent axis force decreases when internal pressure increases, equivalent axis force increases when external pressure increases; increase of internal pressure and decrease of external pressure may make equivalent axis force negative, even less than critical buckling force.