A new cross-anisotropic elasto-plastic constitutive model is developed based on experimental observations of marine clay from the Gulf of Mexico. Standard triaxial and torsional simple shear tests performed on the aforementioned clay demonstrate that the soil exhibits a cross-anisotropic behavior with lower compressibility in the direction of the deposition than perpendicular to the direction of deposition. A new general cross-anisotropic model for the stress-dependent elastic moduli is presented. In agreement with experimental evidence, the model considers that the Young's modulus and the shear modulus of soil depend on the state of stress, while the three Poisson's ratios are practically constant. The expressions for the stress dependence of the moduli are derived by considering the conservation of energy. Numerical simulations of the undrained elastic reloading demonstrate that the development of pore water pressure depends significantly on the exact representation of the cross-anisotropic elastic parameters. The plastic model is developed based on the assumptions that the material behavior is time independent and that the interaction between mechanical and thermal processes is negligible. The model, having twelve parameters, consists of a failure function, plastic potential function (non-associated flow rule), yield function and hardening law. To describe the degree of cross-anisotropy at failure, a new four-parameter failure criterion is developed. The plastic potential function, having two parameters, determines the directions of the plastic strain increments which are assumed independent of the stress path leading to the current state of stress. The potential surface expands along its center line and may translate in the stress space. The yield criteria are associated with and derived from surfaces of constant plastic work. The yield-plastic work relation requires six parameters in which four parameters define the yield function and two parameters define the plastic work equation. For the special case of isotropic soil, all of the functions may be reduced to those of Lade's isotropic elasto-plastic model. Most of the elastic and plastic parameters can be easily determined by experimental results from standard triaxial tests, but a few parameters need advanced tests such as the torsional simple shear test on hollow cylinder specimens and the cubic triaxial test. Comparisons between results from computer simulation of tests and actual experimental data showed that the model is satisfactory in predicting the behavior of the tested clay under torsional simple shear and conventional triaxial compression and extension tests.