Abstract: Based on the sudden jump of deformation in unstable failure of rock under the soft loading condition, the deformation time curve of rock specimen was studied. The system composed of rock specimen and machine was studied by using a cusp catastrophic model. The result shows that the sudden jumps of deformation of rock specimens obtained by the two ways changed with the same trend. The deformation time and load time curves of rock specimens were measured by using HP 7090A Plot Measurement system under unstable condition. The experimental results are fairly in agreement with the theoretical consideration proposed and verified reliability of catastrophe theory in application to the study of rock.