The hydrostatic mapping function, m(ϵ), describes the dependence of the hydrostatic path delay on the elevation angle ϵ. We have developed a simple mapping function, where the only free parameter is an effective height of the atmosphere, Hatm, corresponding to about the first two scale heights above the surface. The value of m(ϵ) is given by the ratio of the straight-line ray path length within height Hatm to height Hatm itself. We used simulated delays at GPS (Global Positioning System) frequencies derived from high resolution ECMWF (European Centre for Medium-Range Weather Forecasts) atmospheric analysis fields to assess the performance of the geometric mapping function relative to well established ones (the Davis, Niell, and Herring mapping functions, respectively). At elevations >6¿ the new mapping function generally exhibits, based on a single parameter, a performance comparable to or better than the other mapping functions.