Abstract Within a microplane theory framework, a model has been developed to simulate the response of sandy soils subjected to non-proportional loading, which occurs in geotechnical engineering. The microplane framework assumes that macroscopic deformations originate with the deformations in the vicinity of planes between particles. The strength and stiffness properties on the various microplanes depend on stress level and the Mohr–Coulomb criterion. To simulate dilatancy due to shear, we introduce a stress–dilatancy relationship on each microplane. Both the microplane strength and the stress–dilatancy relationship incorporate critical state concepts through a state parameter. The model simulations are compared to data obtained in directional shear cell experiments. The model can satisfactorily simulate both distortional and volumetric response of sands subjected to non-proportional loading.