Many geotechnical problems involve the rotation of principal stress and strain directions in the ground. To assess the fundamental behaviour of soils under such conditions, a Hollow Cylinder Torsional Apparatus (HCTA) with independent controls and accurate measurements of the component stresses and strains is required. The crucial characteristic of this apparatus is the possibility of combining axial load, torque and internal and external pressures in a controlled way. These four elements can generate every state of stress-strain in a hollow cylinder specimen. An experimental testing programme on Hostun sand has been proposed using a Hollow Cylinder Torsional Apparatus. Behaviour characteristics in the small strain and medium strain domains under the complex stress states, which are accessible with this apparatus, will particularly be explored. An accurate evaluation of soil stiffness for this strain domain is essential when prediction of instantaneous deformation of ground and displacement of structures under seismic loading are considered.