The paper is focused on a class of boundary value problems of solid mechanics and granular media mechanics with spatially uniform distributions of strain and velocities. Boundary conditions for such distributions are used in numerical experiments. On this basis, a method of affine transformations is elaborated to allow an equivalent continuum model for a given discrete elements model to be developed. Numerically implemented hypoplastic model of a granular medium is presented for cases of both simple shear loading and complex loading with continuous rotation of principal strain axes. It is demonstrated that the model provides good quantitative and qualitative approximation for dilatancy and level of stress. Coaxiality of stress, strain and velocity tensors leads to model predictions close to results describing the behavior of viscous fluid. Numerical implementation of granular media complex loading with continuous rotation of principal strain axes is developed on the basis of discrete elements method. It is shown that the choice of linear forms of particle interaction potentials results in a medium with properties fit to properties of a continuum model for granular media with internal friction and dilatancy. Examples of numerical simulations are provided.