A new analytical solution of an isothermal, Newtonian flow in a single screw extruder with a finite channel is developed with the actual boundary conditions encountered. Down channel velocity distributions are presented in three-dimensional plots. The boundary conditions, velocity distributions, and screw characteristics predicted by the new solution are tested using the experimental data from published literature (Choo et at, 1980, Polymer Engineering and Science, 29 349-56; Griffith, 1962, Industrial and Engineering Chemistry Fundamentals, 1, 180-7). The results ave found to be move accurate than existing theories (Rowell & Finlayson, 1922, Engineering, 126, 249-87; Tadmor & Gogos, 1979, Principles of polymer Processing, Wiley; Rauwendaal, 1986, Polymer Extrusion, Hanser).