Based on exprimental and theretical analysis, the authors propose a new failure criterion for uniaxial and triaxial compression tests. The mechanism for the failure is disturbance of the volume or density continuity caused by the failure. The criterion will be helpeful to find its application to the automatic control of the above mentioned tests. Moreover, the influence of the confining pressure of the rubber membrane case on the soil uniaxial and triaxial compression tests is also discussed. A calculation method is suggested to correct the calculation of cohesion.