In this study, the finite element numerical modelling of 2D shaft sections in a Hoek-Brown medium are carried out in a non-hydrostatic stress state in an attempt to predict pressures developing around mine shafts. An iterative process of applying support pressure until observing no failure zone around the shaft is used to simulate the required lining support pressure for different shaft models. Later, regression analysis is carried out to find a generic shaft pressure equation representing the rock mass and the stress state. Finally, the developed pressure equation which shows a good agreement with a case study is used in elastic "thick-walled cylinder" equation to calculate the lining thickness required to prevent the development of a failure zone around the shaft. At the end of the study, a user-friendly object-oriented computer program "Shaft 2D" is developed to simplify the rigorous shaft lining thickness calculation process. (C) 2016 Published by Elsevier B.V. on behalf of China University of Mining & Technology.