A three-dimensional modeling of the transporting elements in a self-wiping corotating twin-screw extruder has been carried out by using the finite element package Sepran (1). This simulation uses the 3D geometry of the channel rolled over the twin-screw, which consists of the intermeshing and normal areas. The flow profile, the backflow volume, the pressure buildup, the shear and elongation rates, and the adiabatic axial temperature gradient have been calculated by solving the Navier-Stokes equations and the continuity equation for a Newtonian fluid. These results are given for different extruder parameters such as the throughput of the extruder, the rotation speed of the screws and the helix angle of the screws to better understand the influence of different extruder configurations. This study belongs to a program of research on the self-wiping corotating twin-screw extruder that also includes the modeling of the kneading elements (Part II) and, in the future, the study of scale-up and heat transfer.