In this paper, we present two new head-modeling methods and discuss their use to study head-saturation effects. One is a nonlinear multiple-subdomain finite-element method, and the other augments the first by the use of a boundary-integral method to calculate the magnetic field’s density and gradient in the medium from potentials at the head-medium interface. These two methods allow us to calculate efficiently and accurately (less than 5% errors) the head fields and gradients resulting for various models of head saturation. A modified Williams–Comstock model for thick, longitudinally oriented media is used to estimate relative signal output for three example tapes of different magnetic properties. If ferrite gap faces are assumed contaminated or damaged during head construction such that 4πMs drops to around 3750 G, then saturation losses of about 8 dB result. This agrees with Jeffers’s measurements [Proc. IEEE 74, 1540 (1986)] comparing Sendust-tipped and ferrite heads with gap lengths of 0.3 μm.