Geometric distributions of fractures or discontinuities control the behaviour, and limit the strength and the stability of rock masses where the best stabilization and improvement method for that rock mass could be achieved based on favourable discontinuity geometry. This study introduces an algorithm named 'Stochastic Geometry Model of Fractures Network in Tunnels (SGMFNT)', which was developed with the MA THEMATICA software. The SGMFNT method provides a fractures geometric distribution database to aid discontinuous rock mass stability analysis by block modelling codes. This algorithm increased the accuracy of the discontinuity model based on the Heliot and Baecher models in a 2D space. The SGMFNT that was used in two of the sectors of the Kani-Sib water conveyance tunnel in the west Azerbaijan province, Iran has successfully provided the rock mass geometrical discontinuity model for this case study.