We use numerical methods to solve the two-dimensional tomographic source problem, and we investigate the accuracy of the slip velocity reconstruction achieved. We perform the inversions of the source time functions (STFs) considering both the effect of errors in the source-station azimuths and the uncertainties introduced by using an empirical Green function scheme as a method for computing the STF. We also investigate the dependence of the results on the number and arrangement of the stations. We adopt two different iterative schemes to invert the Radon transform. The numerical tests show that even small errors in the data can have significant effect on the results, pointing out the ill-posedness of the considered inverse problem. The results also show that the introduction in the algorithm of a priori information, such as positivity or boundary for the reconstruction domain, improves the quality of the reconstructions and allows retrieval of qualitative information about the rupture process even in the case of poor azimuthal coverage. We test our method on two recorded earthquakes. The first one occurred in southern California on May 1, 1985 (ML=2.4), and our results show good agreement with earlier studies. The second one, which occurred in northwestern Italy on August 23, 1996 (MD=2.9), appears to involve a more complex, possibly bilateral rupture. The inability of the Radon approach to resolve the bilateral rupture, as we show using a synthetic test, does not allow us to draw any definitive conclusion about this earthquake. ¿ 2001 American Geophysical Union