The Cambridge True Triaxial Apparatus permits samples of soil to be tested with independent variation of the three principal stresses. A feedback system, based on a small computer, has been attached to the apparatus and this enables any three-dimensional stress path that is desired to be followed accurately. Three groups of stress paths are described here, all applied with constant mean normal stress to samples of isotropically consolidated kaolin. These paths are used to examine the success with which two numerical models of soil behaviour (the so called Cam clay and microstructural models) are able to predict the experimentally observed behaviour for these more complicated conditions of stress. (Both models have previously been used with some success for axisymmetric conditions of stress and strain). The assessment of the success of the predictions will depend on the use for which the models are required. Neither model is very successful for stress paths in which the octahedral stress ratio decreases. For paths on which this stress ratio is increasing both models are moderately successful in their predictions.