A two-dimensional finite-element method was used to model a horizontal magnetoresistive head in order to test the fabrication design parameters. The device consists of two magnetoresistive elements placed closely together and parallel to the plane of the media, following a design of Chapman, Heim, and Williams [IEEE Trans. Magn. MAG-25, 3689 (1989)]. A single transition in the media was moved, in steps, past the head. The electrical signal strength and pulse width, due to this transition, were studied as a function of the shield permeability, thickness and shield gap, the sensor-sensor distance, the flying height, and sensor-shield distance. The width of the pulse did not show appreciable change with shield thickness, permeability, or shield gap size, although the signal strength changed significantly. A thin shield (1000 angstrom) of moderately low permeability (2000) is therefore preferred. The signal fell off almost exponentially with flying height and sensor-shield separation. The situation where no shield was present was also simulated and showed a reasonably narrow pulse with a large undershoot and a long tail. These results indicate the horizontal head suggested by Chapman and co-workers may in fact provide good readback resolution with a thin shield or perhaps no shield whatsoever.