Considerable practical knowledge and effective use of empirical evidence is required in the design of tunnel support systems. In many instances, it is unclear how individual support elements interact with fractured rock and which elements of the support system are critical in controlling and containing the movement of material proximate to the excavation. The present paper outlines a displacement discontinuity approach that allows the coupling of surface constraints, in the form of liner or mesh material, to an explicit representation of time-dependent rock discontinuity creep movements. The method is illustrated for a simple square-shaped tunnel profile in which the fracture zone is mobilised by an imposed stress field. A crucial aspect of the model is the computational treatment of the coupling between the liner material and the representation of the fractured rock mass. This allows the response of the liner material to be assessed quantitatively in terms of the possible reduction of movement in the rock mass. The importance of installing the liner timeously after the excavation is formed is illustrated in a specific example. A number of computational difficulties in simulating liner-rock interaction mechanisms are identifie.