A three-dimensional (3D) reciprocity based model of the perpendicular read process with a soft underlayer is presented. In 3D with finite track width, the read flux does not decay to zero because flux is always entering the reader from the field caused by a nonvanishing curl of the magnetization. As the reader is moved off track, the signal amplitude and resolution decrease, and at some off track position there is a reversal in the sign. A comparison of the reciprocity based reader model with a micromagnetic CPP reader model shows excellent agreement both on and off track. (C) 2002 American Institute of Physics.