Abstract: The paper presents the numerical and experimental study of shearing interferometric tomography for Richtmyer-Meshkov instability diagnosis. On the basis of simultaneous algebraic reconstruction technique (SART), a method is presented to compute the projection coefficient matrix using specific projection directions and different sampling interval for each direction. The symmetrical projection and projection ray regularity simplify the computing process of the conventional SART. The reconstruction of the density field of a gas cylinder was performed. The numerical results show that four-directional computer tomography（CT） can reconstruct the density field in the early stage of evolution and eight-directional CT has the maximal error less than 17% in the middle stage of evolution. Three shearing interferometers were used to measure the gas cylinder density in shock tube from three different directions. The phase distribution deduced from the interferograms basically coincides with the theoretical prediction. The results of numerical computation and experiment indicate that shearing interferometric tomography may be a useful tool for the study of Richtmyer-Meshkov instability.