The extrusion process for aqueous-based ceramic pastes is complex due to the non-Newtonian behavior of these pastes. In this study, the extrusion process is modeled by characterizing the ceramic paste viscosity using a modified Herschel–Bulkley model. The steady-state relationship between plunger velocity and extrusion force is built based on this viscosity model and the Navier–Stokes equations. The influence of air, which may be trapped in the paste during the paste preparation and loading processes, is also examined as it significantly affects the dynamic response of the extrusion force. Combining these effects with the steady-state extrusion model, a constitutive law for the extrusion process of aqueous-based ceramic pastes is created. Because of the compressibility introduced by the trapped air, the dynamic response of the extrusion force is described by a first-order nonlinear equation when plunger velocity is taken as an input. It is shown that the extrusion response time depends on the amount of air in the extruder and the magnitude of the extrusion force. Air bubble release, a phenomenon that causes the extrusion force to suddenly drop due to the change of paste volume in the nozzle, is analyzed based on the developed constitutive model.