A simple 2-dimensional model based on stochastic theory has been applied to simulate time-dependent failure of an underground roadway in mine. In the calculation, FEM technique is used, and the obtained results are compared with the resultsmeasured at a mine in Akita prefecture. The road way considered in this study is U-shaped and supported by rockbolts installedin a square grid pattern at 1m interval. The calculated results of convergence and extension indicate a fairly good coincidence, at least in qualitative means, with measured ones.By the virtue of the model versatility, the simulation has been carried out for various conditions changing bolt length, diameter, setting-time and so on. Through the calculation, it is found that grouted rockbolt support can retard the failure ingreat extent and are much superior to conventional point anchored bolt or steel arch support.It can be said that the model showed a potential for application purpose. Simplicity of this model requires a minimummodification of a standard FEM program and also minimum experimental work to obtain necessary parameters. Application ofthis model to tunnel, dam, slope, underground storage and plant may be possible.