Interpolation of elevation data from fluvially eroded topography is difficult for available methods because of the inherent roughness and drainage properties of the fine-scale surface. We propose a new method that produces an interpolation surface by adapting a simulated topography to a given set of point elevation data. The simulated surface is produced by a simple model that rapidly simulates topography in dynamic equilibrium including the effects of tectonic uplift, fluvial incision, and hillslope diffusion. Agreement between the simulated topography and the elevation data is improved by iteratively adjusting a spatially varying erodability parameter. When the iterative procedure terminates, the simulated surface is in close but not in exact agreement with the observations. Exact agreement can usually be produced by distorting the simulated surface in a way that does not introduce local depressions. Interpolation surfaces generated by the proposed method have realistic drainage patterns without unrealistic depressions. In addition, the textural properties of the interpolation surfaces, including the distributions of slopes and curvatures, are better than those generated by other interpolation methods.