In one form of building structure, trim installations are applied around window or door frame openings and at internal or external corners of a building. The trim serves both an aesthetic purpose in adding a decorative feature to building envelopes and also adds an additional weatherproofing purpose in allowing for more complete weatherproofing of building envelope corners and openings. The present invention relates to a concealed fastening building finishing element system that enables concealed fastening of finishing elements such as trim components, fascia boards, frieze boards, belly band boards, and the like to an underlying structure and to the fixings used in these systems. The invention is particularly useful with trim elements around window and door frame openings and at building corners.