Self-tapping screws are efficient and flexible fasteners, applicable for many types of connections. Investigations on axially loaded groups of screws pointed out, that small spacing between the screws lead to block shear failure mode. So far, block and plug shear failure mode are only analysed for laterally loaded fasteners. Corresponding models cannot be simple transferred to primary axially loaded screws, because of their load insertion continuously along the effective thread featuring a thread-fibre angle perpendicular or with an angle to grain. Results gained by means of two different test configurations, with constant 90° thread-fibre angle but different configurations of group of screws and support conditions are presented. A block shear model is presented, and for mean values for stiffness and strength properties as model parameters are discussed together with values for parameters related to the force distribution over the effective thread length for the first test configuration. Agreement between model and test results was found on a conservative basis. As outlook, considerations of additional bending stresses as well as parameter optimisation are seen as prerequisites and next steps for further model improvement and practicality.