The validity of the stress dilatancy equation for representing the small stress ratio state response of sand is examined. Test equipment development and procedures that were followed aimed at precise loading control and reliable monitoring of small displacements and volume changes. A variety of load controlled stress paths were applied to conventional triaxial test samples of Ottawa sand. The results obtained show that at small stress ratio states a relationship between stress state and strain increment direction as prescribed by the stress dilatancy equation does not apply. Stress increment directions were found to be related to strain increment directions for low stress ratio states. The relationship has some resemblance to the behavior of a cross anisotropic elastic material with a stiffer vertical to radial response. The range of low stress ratio states over which a stress dilatancy relationship does not apply tends to increase with density. In stress ratio regions where the stress dilatancy equation began to apply, the relationship between R and D tends toward KCV with increasing confining stress for conventional triaxial but not for constant mean normal stress paths.