This paper addresses the computational modelling of rolling shear cracks in cross-laminated timber structures. In order to predict the structural response, four spatial scales are interlinked within a multi-scale modelling framework. Material information is taken from the wood cell-wall at the order of few nanometers, wood fibres with dimensions of some micrometers and growth rings described by a few millimeters. A computational homogenisation scheme is adopted to determine the effective mechanical properties at each scale. The homogenised mechanical properties are then used to analyse the fourth (structural) scale represented by a cross-laminated timber plate with dimensions of the order of the meter. In order to simulate the cracking in the material, a cohesive zone model is adopted at the homogenised macroscopic scale. This approach allows us to model interlaminar and inter-fibre cracks. Our numerical simulations reveal the potential predictive capabilities of the present approach to investigate further wood and other natural materials.