In this study, the triaxial behaviour of an unsaturated soil was analyzed by Bishop stress descriptions. $K_0$ stress paths and those final values were independent of matric suctions after describing by the Bishop stress. The failure criteria could be defined uniquely by the Bishop stress and were also independent of matric suctions. In the low level of matric suctions the failure criteria have a linear relationship and the estimated criterion fits the measured accurately. The variable ${chi}$ for describing the Bishop stress was a constant theoretically under the low level of matric suctions. The suction stress could be defined at zero deviatoric stress in the failure criteria and increased linearly with respect to matric suctions in both the theory and the experiments.