Using Nishihara model to describe the rheological characteristics of dual-pore-fracture media, a method is theoretically presented to determine the rheological parameters and strength indices of the media. The plane finite element scheme for solving the transient elastic-viscoelastic-viscoplastic problems is built, and the corresponding calculation program is developed. Aiming at the two conditions of surrounding rock mass from a rectangular underground cavern, in which the first rock mass is fractured by two sets of joints (a dual medium) and the second one is intact (a single medium); the displacements, stresses and plastic zones in the surrounding rock masses are analysed and compared numerically. The results show that when compared with the case of single medium, the deformation modulus, cohesion and internal friction angle of the dual medium decrease, so the corresponding displacements and plastic zones in the surrounding rock mass develop with time elapsing obviously. And there is a greater difference between the stress distributions of these two cases, especially the difference between the maximum principal stress and the minor principal stress in the surrounding rock mass, which is larger for the case of dual medium. Therefore, the possibility of rock mass failure is increased.