Cross laminated timber (CLT) and self-tapping screws have strongly dominated the latest developments in timber engineering. Although knowledge of connection techniques in traditional light-frame structures can be applied to solid timber constructions with CLT, there are some product specifics requiring additional attention; for example in positioning of fasteners, differentiation in the side face and narrow face of the panels and the influence of potential gaps. The load–displacement behaviour of single, axially-loaded self-tapping screws positioned in the narrow face of CLT and failing in withdrawal was investigated. For the first time a multivariate probabilistic model was formulated together with models relating the parameters with the thread-fibre angle and the density. Different types and widths of gaps, initial slip and / or delayed stiffening as well as softening after exceeding of the maximum load can be considered. Beyond the scope of this contribution, the probabilistic model is seen as a worthwhile basis for investigations into the withdrawal behaviour of primary axially loaded, compact groups of screws positioned in timber products and subjected to withdrawal failure.