The stability and associated design of roof reinforcement requirements of tunnels driven in United Kingdom Coal Measures strata is directly related to the engineering characteristics of the immediate roof lithology and the effects of redistribution of the in-situ stress. Numerical modelling carried out by the authors has been used to simulate the widely observed detrimental effects of both high horizontal stress and weak immediate roof lithology on tunnel roof stability. Different numerical modelling techniques, such as continuum, discontinuum and hybrid finite element-discrete element codes, have been used to model the deformational behaviour of Coal Measures strata and are discussed in the context of specific case examples to highlight their application and suitability for modelling of weak rock. The modelled results demonstrate that the thickness of the relatively weak mudstone in the roof of the tunnel has a significant influence on the extent of failure and, ultimately, the need for additional reinforcement. (C) 2011 Elsevier B.V. All rights reserved.