In single-screw extrusion the simulation of the plasticizing process by meants of software tools becomes more and more important. These programs need mathematical models that have to be improved continuously to simulate the process values realistically. A two-part article presents an analytical approach to calculate the pressure/throughput and drive power behaviour of wall-slipping polymers in the melting section of Single-screw plasticizing units. The investigations that are conducted are based on the notion commonly found in the literature of a melt film forming between the barrel and a compact solid bed, with the simultaneous development of a melt pool. As boundary condition for describing the wall slippage, a critical shear stress, as of which a slippage process commences, and also it slippage-velocity-dependent shear stress is assumed. In this first part of the publication, the investigations focus on the processes that take place in the melt film. A new model is developed for describing the process behaviour in this area.