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SUMMARYA rheological model which is able to explain the delayed failure phenomenon has been proposed and applied to the analysis of the time dependent behaviour of deep tunnels. The model is the three element Voigt type before yielding and becomes the five element Voigt type after yielding. This means that the stiffness of the model is decreased by yielding. It is assumed that the yielding takes place when the stored elastic energy density of distortion reaches a certain maximum value. Some experiments to determine material constants are proposed. The numerical results clearly exhibited a delayed failure state of the rock masses around the tunnel surface. It was found that the extension of the yielding zone due to tunnel excavation depends on the opening method.