In the single-screw extruder, the vibration force field is applied to the solids conveying process by the axial vibration of the screw and the novel concept on the solids conveying process being strengthened with the vibration force field has been brought forward in this study. We establish the mathematical model that describes the solids conveying process with the vibration force field and obtain the approximative analytical solutions of the pressure and velocity of the solids conveying in the down-channel. In the new theory, if the screw has no axial vibration the solids conveying pressure is the same as that of the Darnell and Mol theory, but the density and velocity of solids conveying along the screw channel is variable, which has modified the Darnell and Mol theory in which the density and velocity of the solids conveying along the screw channel was considered invariable. The results reveal that the axial vibration of the screw can increase the average pressure of solids conveying, decrease the channel length of the solids conveying section and increase the solids conveying angle. (c) 2006 Wiley Periodicals, Inc.