Discrete element modelling is commonly used for particle-scale modelling of granular or particulate materials. Developing a DEM model requires the determination of a number of micro-structural parameters, including the particle contact stiffness and the particle-particle friction. These parameters cannot easily be measured in the laboratory or directly related to measurable, physical material parameters. Therefore, a calibration process is typically used to determine the values for use in simulations of physical systems. This paper focuses on how to define the particle stiffness for the discrete element modelling in order to perform realistic simulations of granular materials in the case of linear contact model. For that, laboratory tests and numerical discrete element modelling of triaxial compression tests have been carried out on two different non-cohesive soils i.e. poorly graded fine sand and gap graded coarse sand. The results of experimental tests are used to calibrate the numerical model. It is found that the numerical results are qualitatively and quantitatively in good agreement with the laboratory tests results. Moreover, the results show that the stress dependent of soil behaviour can be reproduced well by assigning the particle stiffness as a function of the particle size particularly for gap graded soil.