Due to the expected future climate change, glacier ice as a resource will be further diminished and its sea-level rise contribution further increased. A key for a more accurate determination of future glacier evolution is to improve our currently sparse knowledge on glacier bedrock topography. Here, we present a simplified method implemented in a geographic information system to approximate subglacial topography at a regional scale from spatial interpolation of local ice thickness values. The latter were derived from an ice-dynamical approach, which relates glacier thickness to its local surface slope, total vertical extent, and basal shear stress. The only input data required are glacier outlines, a set of central branch lines, and a digital elevation model (DEM). The modeled glacier beds are in good agreement with other, more complex modeling approaches and direct measurements. The observed local deviations can be explained with the sensitive dependence of our approach on the surface slope and the different methods used for spatial interpolation. The mean glacier thickness derived here for a sample of 40 glaciers in the Swiss Alps is slightly smaller than that derived from a similar, but scalar approach. Further adjustments of the data processing are possible to achieve agreement with available validation data. However, despite its local inaccuracies, the resulting DEM without glaciers can facilitate several applications such as the detection of overdeepenings or the modeling of future glacier evolution.