By excavating an underground space, the state of stress and displacement in the surrounding medium are changed in comparison to the inital state. As time passes, the variation of the displacement mainly depends on the creep behaviour of the hosting rock mass. In this paper, an elasto-viscoplastic creep model is proposed. In the proposed model, the main purpose is to consider plastic deformations increasing with time. The viscoplastic behaviour of rocks plays a key role in the tunnelling works, especially for deep tunnels subjected to large in situ stresses. Using non-linear Hoek-Brown yield criterion in a creep model is the other important aim of this paper, which eliminates estimating specific equivalent Mohr-Coulomb strength parameters from the Hoek-Brown parameters. The equations related to the proposed model are derived and then, to reach a numerical solution of the equations, the finite difference software (FLAC2D-FISH Editor) is used. The application of the proposed model is illustrated through an example analyzed numerically using the finite difference software FLAC2D.

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