I present an algorithm that uses cross-dipole wireline data only in order to estimate the HTI stiffness tensor for sandstone formations under in-situ asymmetric lateral (azimuthal) stress conditions.The algorithm is based on the generalization of terms “excess compliance” and “fracture weakness” developed within the linear slip interface theory for fractured rocks and is applied here to describe the effect of grain contacts in loose sandstones.I introduce the term “plane of weakness” being oriented (aligned) orthogonal to theminimal horizontal principal stress direction in order to describe the overall effective weakness of sandstone caused by the different principal stresses.For the quantification of this phenomenon I use the anisotropic Gassmann model.As a result I am able to calculate a HTI stiffness tensor for the interval length of a saturated sandstone formation and the respective Thomsen’s parameters.The input data required for these calculations have to be provided by wireline logging and will consist of porosity,density,P-wave velocity,fast and slow shear wave velocities and oil-water saturation ratio.The algorithm in its current form is applicable to sandstone reservoirs only.Its limitation is based on two assumptions,which state that all the measured anisotropy is induced by the present stress in sandstone and that the unstressed sandstone would be nearly isotropic.From a technical viewpoint this algorithm can be implemented fairly easily in data acquisition and interpretation software relying on correct estimation of anisotropy parameters.It is also cheap because it does not require any additional measurements apart from the cross-dipole logging. I present an algorithm that uses cross-dipole wireline data only in order to estimate the HTI stiffness tensor for sandstone formations under-situ asymmetric lateral (azimuthal) stress conditions. The algorithm is based on the generalization of terms “excess compliance ” and “fracture weakness ” developed within the linear slip interface theory for fractured rocks and is applied here to describe the effect of grain contacts in loose sandstones. I introduce the term “plane of weakness ” being oriented (aligned) orthogonal to theminimal horizontal principal stress direction in order to describe the overall effective weakness of sandstone caused by the different principal stresses. For the quantification of this phenomenon I use the anisotropic Gassmann model. As a result I am able to calculate a HTI stiffness tensor for the interval length of a saturated sandstone formation and the respective Thomsen’s parameters. input data required for these calculations have to be provided by wir eline logging and will consist of porosity, density, P-wave velocity, fast and slow shear wave velocities and oil-water saturation ratio. The algorithm in its current form is applicable to sandstone reservoirs only. It is based on two assumptions, which state that all the measured anisotropy is induced by the present stress in sandstone and that the unstressed sandstone would be nearly isotropic. Focus a technical viewpoint this algorithm can be implemented fairly easily in data acquisition and interpretation software relying on correct estimation of anisotropy parameters. is also cheap because it does not require any additional measurements apart from the cross-dipole logging.