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An explicit integration scheme that combines improved accuracy and reduced computational cost is presented herein, for the implementation of the NTUA-Sand bounding surface constitutive model into the Finite Difference Code FLAC (Itasca, 2011). The proposed integration algorithm automatically switches between a modified-Euler integration scheme with error-control and sub-stepping (Sloan et al, 2001), and the much simpler and computationally effective first-order (single-step) Euler integration, based on the local degree of non-linearity of the stress-strain relationship. The non-linearity is estimated from the difference between the stress increments of two consecutive steps, which is consequently compared against a given tolerance value, in order to select the appropriate integration scheme. The computational accuracy of the proposed integration algorithm is evaluated using the iso-error maps procedure, while its computational efficiency is demonstrated through its application, in element level, for the prediction of stresses in a given undrained shear strain path.