A homogenous melt is the prerequisite to achieve the demanded product quality in single screw plasticising technology At higher screw speeds and mass flow rates solid particles can occur in the melt. Dispersive mixing elements are often used to improve the melt quality. Calculation models are necessary for designing mixing elements in the right way. A new model for the often used fluted mixing sections like axial and spiral Maddock-elements and Z-elements is presented in this paper. The calculation model is reduced to a single pair of inlet and outlet flute, connected by the shearing gap. Especially in spiral Maddock mixers the longitudinal flow in the flutes is a combined pressure and drag flow but in axial Maddock mixers pure pressure flow occurs. In the shearing gap a combined pressure and drag flow can occur The leakage flow through the flight clearance is also considered. Geometry functions are introduced for considering the rectangular or circular segment shaped cross section of the flutes. The viscosity is shear rate and temperature dependent, the channel height as well as the channel width can vary along the mixing element. The model allows the calculation of the longitudinal pressure profile in the inlet and outlet flutes, the total. pressure drop and the shear stress distribution in the shearing gap. Mixing sections sometimes show a too high pressure consumption and insufficient shearing efficiency. Therefore a geometry optimization method for axial Maddock mixing heads is presented in this paper.