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Interferometric synthetic aperture radar (InSAR) techniques are today applied in many areas of remote sensing, ranging from digital elevation model (DEM) generation to surface motion mapping and InSAR tomography. To enhance the understanding of the InSAR mapping process and to test new algorithms, accurate tools for the simulation of the topographic InSAR phase are necessary. Whereas the equations for the interferometric phase of a given DEM are well known, the actual implementation is tedious. Furthermore, a straightforward implementation would take far more computation time than all the other InSAR processing steps put together. This paper presents a novel algorithm for the efficient simulation of the InSAR phase, taking into account the special problems in mountainous terrain. Simulation results are compared to and illustrated with real data from the European Remote Sensing satellite (ERS-1/2) tandem mission and the Shuttle Radar Topography Mission (SRTM). Accuracy estimates for the phase simulation are given for different terrain types. The algorithm is described in enough detail that it can be implemented as a general-purpose tool for the accurate simulation of interferograms with virtually unlimited size, taking no more processing time than other InSAR processing steps. The algorithm in the presented form is used operationally within the interferometry software GENESIS to support the processing of SRTM/X-SAR data at the German Aerospace Center (DLR).