 New true-triaxial experiments of sandstone compaction under non-hydrostatic load 19 demonstrate directional (non-isotropic) compaction. 20  We introduce a directional compaction model that extends the isotropic Athy’s law. 21  We apply the directional compaction model to study compaction and elastic stress 22 distribution in sedimentary basins. 23 24 Abstract 25 Compaction is usually addressed as an isotropic process that ignores the effects of 26 deviatoric stress components. This allows a particularly helpful simplification of 27 hydromechanical coupling. In general, stress in the crust is not isotropic and may lead to 28 directional compaction. In this study, we present new true-triaxial experiments of 29 Sheshminskaya sandstone, demonstrating the assumption of isotropic compaction under 30 anisotropic load leads to significant errors. We extend the isotropic Athy’s law to directional 31 compaction model and show that compaction in one direction is associated with decompaction in 32 perpendicular directions, including accumulation of anisotropic irreversible strains. The 33 directional compaction model accurately simulates the measured compaction values of the 34 Sheshminskaya sandstone under sequential loading in three different directions. We apply the 35 directional compaction model to study the effects of vertical compaction on horizontal stress and 36 overall compaction in sedimentary basins. In the case of dominant effect of deviatoric stress, 37 vertical compaction is one order of magnitude greater than the horizontal decompaction. The 38 compaction tensor is suggested to affect the permeability anisotropy. During burial of sediments, 39 vertical compaction leads to significant vertical permeability reduction, whereas small horizontal 40 decompaction leaves high horizontal permeability values. 41 42 Plain Language Summary 43 Sediments in evolving basins compact under the weight of the accumulating overburden. This 44 process considerably reduces porosity and permeability and it is crusial for oil, gas, and water 45 reservoir management. Various simple and advanced models exist for mechanisms of uniform 46 and non-uniform sediment compaction. These models address the compaction as an isotropic 47 process that ignores effects of different horizontal and vertical stress components. New true-48 triaxial experimental results demonstrate that assuming isotropic compaction under anisotropic 49 load leads to significant errors. Complex stress distribution acting during the burial of sediments 50 leads to significant difference between vertical compaction and permeability reduction, whereas 51 small horizontal decompaction leaves high horizontal permeability values. 52 53