The present study is an attempt to model abyssal hill topography, i.e., the randomly varying topography that is superimposed on the subsidence of the ocean floor due to thermal contraction. We assume that abyssal hill topography is created by faulting, and that it can be represented as the convolution of a series of stochastic fault offsets with a fault impulse response. As a constraint, the power spectrum of the model-generated topography will have to resemble the power spectrum of a profile of abyssal hill topography across a typical slow spreading ridge such as found in the South Atlantic. Using a series of fault offsets positively correlated in space and fault impulse responses limited to a finite width w, profiles that statistically resemble abyssal hill topography have been generated. If the fault offsets are constrained to be positive, i.e., to cause uplift, the synthetic profiles contain a steady state depression at the axis. The fit of the synthetically derived topography to the observed topography is very sensitive to the width w of the fault impulse response. Our results suggest that the effects of a faulting event must be limited to distances of about 3.5 km and that tectonic activity must take place in the immediate vicinity of the inner wall of the axial valley. If faulting is indeed the process that creates abyssal hill topography, the best fit flexural impulse response to faulting implies a flexural rigidity of 5¿1017 N m. If instead constructional volcanism contributes significantly to the topography, our study suggests that the emplacement of volcanic constructions must also take place within a narrow width w about the axis. ¿ American Geophysical Union 1989