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This paper presents an approach for the automatic parameter calibration (AC) of a hypoplastic constitutive soil model. The calibration software developed in this work simplifies the parameter calibration, reduces the subjective “human” factor on the calibration result and lowers the entry hurdle for the use of the hypoplastic constitutive model. The performance of the software was demonstrated by comparing automatically calibrated parameter sets for two sands and their related simulations of the underlying experimental data with simulations using two reference parameter sets. The first reference parameter set was calibrated the classical way, "by hand", and the second was calibrated using the AC tool ExCalibre. Two different optimization methods were used, namely the Differential Evolution (DE) and the Particle Swarm Optimization (PSO). The simulations performed with the parameters obtained from the AC agree well with the experimental data and show improvements over the reference parameter sets. With respect to the optimization method, the performance of the DE proved superior to that of the PSO. Various measures of comparison were examined to quantify the discrepancy between experiment and simulation. By repeating 500 calibration runs, the dispersion of parameters was determined and correlations between different parameters of the hypoplastic model were found.