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This paper presents an innovate approach to simulate the stress-strain behaviour of sands subjected to large amplitude regular cyclic loading. New prediction correlations were derived for damping ratio (D) and shear modulus (G) of sand utilizing linear genetic programming (LGP) methodology. The correlations were developed using several cyclic torsional simple shear test results. In order to formulate D and G, new equations were developed to simulate hysteresis strain-stress curves and maximum shear stress (τ max ) at different loading cycles. A genetic algorithm analysis was performed to optimize the parameters of the proposed formulation for stress-strain relationship. A total of 746 records were extracted from the simple shear test results to develop the τ max predictive model. Sensitivity and parametric analyses were conducted to verify the results. To investigate the applicability of the models, they were employed to simulate the stress-strain curves of portions of test results that were not included in the analysis. The LGP method precisely characterizes the complex hysteresis behaviour of sandy soils resulting in a very good prediction performance. The proposed design equations may be used by designers as efficient tools to determine D and G, specifically when laboratory testing is not possible.