Compaction in sedimentary basins has been traditionally regarded as a one-dimensional process that ignores inelastic deformation in directions orthogonal to the active load. This study presents new experiments with sandstone demonstrating the role of three-dimensional inelastic compaction in cyclic true triaxial compression. The experiments were carried out on the basis of a triaxial independent loading test system in the Laboratory of Geomechanics of the Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Science. The elastic moduli of the material were estimated from the stress-strain curves and the elastic deformations of the sample in each of the three directions were determined. Subtracting the elastic component from the total deformation allowed to show that inelastic compaction of the sandstone is observed in the direction of active loading, whereas in the orthogonal directions there is a expansion of the material. To describe the three-dimensional nature of the compaction, a generalization of Athy law to the tensor case is proposed, taking into account the role of the stress deviator. The compaction tensor and the kinetic equation to describe the evolution of inelastic deformation, starting from the moment of the load application are introduced. On the basis of experiments on cyclic multiaxial compression of sandstone, the identification and verification of the constructed model of tensor compaction were carried out. The possibility of not only qualitative, but also quantitative description of changes in inelastic deformation under complex cyclic triaxial compression is shown.