A mathematical model is developed for a steady-state axi-symmetric upstream flow of a porous disc, in a uniform flow field . The special case of the upstream flow of a windmill, with and without a nacelle, is treated. First, the windmill is considered as a uniform distribution of sources and then as a linear distribution of sources. Solutions for the blade disc o f the wind field upstream are obtained in the form of stream1 ines and velocity vector components. Sample flow patterns upstream o f the blade disc o f the UMass 25 kW wind turbine are presented for several power levels. Documented computer programs applicable to any wind turbine are appended.