Stochastic methods of analysis are useful for quantifying ensemble properties of small-scale bathymetric features such as abyssal hills. In this paper we model the seafloor as a stationary, zero-mean, Gaussian random field completely specified by its autocovariance function. We formulate an anisotropic autocovariance function that has five free parameters describing the amplitude, anisotropic orientation and aspect ratio, characteristic length, and Hausdorff (fractal) dimension of seafloor topography. Parameters estimated from various seafloor regions by an inversion of Sea Beam data indicate that the the seafloor exhibits a wide range of stochastic characteristics within the constraints of the model. Synthetic topography can be generated at arbitrary scale resolution from the Gaussian model using a Fourier method. Color images of these synthetics are usefull for illustrating the stochastic behavior of the model. ¿ American Geophysical Union 1989