The introduction of Cross-laminated Timber (CLT) as an engineered timber product has played a significant role in the considerable progress of timber construction in recent years. Extensive research has been conducted in Europe and more recently in Canada to evaluate the fastening capacity of different types of fasteners in CLT. While ductile capacities calculated using the yield limit equations are quite reliable for fastener resistance in connections, however, they do not take into account the possible brittle failure modes of the connection which could be the governing failure mode in multi-fastener joints. Therefore, a stiffness-based design approach which has already been developed by the authors and verified in LVL, glulam and lumber has been adapted to determine the block-tear out resistance of connections in CLT by considering the effect of perpendicular layers. The comparison between the test results on riveted connections conducted at the University of Auckland (UoA) and at the Karlsruhe Institute of Technology (KIT) and the predictions using the new model and the one developed for uniformly layered timber products show that the proposed model provides higher predictive accuracy and can be used as a design provision to control the brittle failure of wood in CLT connections.