This thesis is a theoretical investigation into the time-dependent behaviour of rock joints. Much of the research work that has been conducted to date in the area of finite element analysis has been involved with the development of special elements to deal with these discontinuities. A comprehensive literature survey is undertaken highlighting some of the significant contributions to the modelling of joints. It is then shown how internal variables can be used to model discontinuities in the rock mass. A finite element formulation is described resulting in a system of equations which can easily be adapted to cope with various constitutive behaviours on the discontinuities. In particular, a viscoplastic relationship; which uses a homogeneous, hyperbolic yield function is adopted. The viscoplastic relationship can be used for both time-dependent (creep) or quasi-static (elasto-plastic) problems. Time-dependent behaviour requires a time integration scheme and therefore a generalised explicit/implicit scheme is chosen. The resulting numerical algorithms are all implemented in the finite element program, NOSTRUM. Various examples are presented to illustrate certain features of both the formulation and the numerical algorithm. Jointed rock beams and a jointed infinite rock mass are modelled assuming plane strain conditions. Reasons are proposed to explain the predicted behaviour. The results of the analysis shows that the internal variable formulation successfully models time-dependent joint movements in a continuous media. The method gives good, qualitative results which agree with observations in deep level mines. It is recommended that quantitative mine observations be used to calibrate the model so that usable predictions of joint movement can be made. This would enable any new developments to be implemented in the model. Further work on implicit methods might allow greater modelling flexibility by reducing computer run times.