The mathematics of emission-computed tomography is applied to the analysis of stereoscopic observations of auroral arcs. The incomplete data problem for three-dimensional computerized tomography, due to the very limited angular range and the small number of observers, is solved by an iterative least squares method. A theoretical example with the projection of two auroral arcs can be reconstructed with projection root-mean-square errors of the order of 1%. Application of noise deteriorates the quality of reconstruction, but with suitable low-pass filtering, root-mean-square errors of less than 5% can be obtained. The agreement between observed and calculated projections, as well as between the original and the reconstructed volume emission distribution, is quantitatively discussed for different observation geometries. With only two observation sites the range of acceptable observation geometries is limited to distances of 25 to 50 km between the observers but depends on the actual location and the morphology of the aurora. Sources of distortion of real auroral observations with intensified CCD cameras are discussed and correction procedures proposed. The complete procedure is applied to a real stereoscopic auroral observation. The correspondence of original pictures and projections of the reconstructed volume is discussed, and emission profiles along magnetic field lines are extracted from the three-dimensionally reconstructed arc. ¿ American Geophysical Union 1996