Abstract: The deformation of roof strata supported by pillars in mined out area was analyzed in consideration of the rheological properties of rock masses and by utilizing the elastic-viscoelastic correspondence principle and numerical Laplace inversion. The roof deflection as a function of time was established, based on which the time-dependent behavior of the roof displacement was elaborated. It is shown that when rock creep properties are taken into account for both the pillars and roof, the roof displacement increases with pro-longing time as expected. Therefore, given a sufficient period of time, the roof deformation can reach a considerable magnitude even for hard rock masses and eventually lead to the collapse of roof strata. As a case, the estimation of failure time was carried out for Xingtai Gypsum Mine in China, in which the feasibility of the proposed method was verified by acceptable agreement between the estimated data and actual field observations.