A series of strain controlled tests have been performed on a two-dimensional analogue granular material, composed of three different sizes of rods, in a special laboratory apparatus which permits full control of plane deformations, including rotation of principal axes. These tests have been designed and used to explore certain constitutive conjectures concerning the mechanical behaviour of granular materials. The results, within the accuracy of the apparatus, show that irrespective of the initial stress history of the material, proportional strain paths lead asymptotically to proportional stress paths. The asymptotic stress path appears independent of the fixed imposed rotation of principal strain axes and at the asymptotic state coaxiality between the principal stress direction and the principal incremental strain direction seems to be reached. A unique relationship between the imposed dilatancy and the corresponding asymptotic stress ratio has been identified.