In numerical models based on the crystal plasticity theory, various rules are implemented to describe hardening on the slip system level. The rules used are often variations of the Mecking-Kocks law, where the statistically stored dislocation density is the single internal variable. The dislocation density evolution equation consists of two terms representing accumulation and annihilation of dislocations. The accumulation term depends on a scalar parameter and an interaction matrix, which describes the contribution of all slip systems to the accumulation of the dislocations on a given slip system. Physically this matrix represents the relative strength of various dislocation locks which form when dislocations from different slip systems interact. The numerical values of the elements of the interaction matrix are rather hard to establish, but this has been done experimentally for different alloys and also based on numerical simulations. The obtained values, found in literature, are very different from each other. We use some new experimental data in an attempt to establish the influence of the numerical values of the elements of the interaction matrix on the hardening of a polycrystal.