The subject of the paper is the modelling of multi-bolted connections that are at the pretensioning stage. Taking a systematic approach to the modelling issue, the connection was treated as a composite of four subsystems: a bolt set, a pair of joined elements and a contact layer between them. The first part of the paper describes experimental studies to determine the contact stiffness of a pair of elements separated from an exemplary asymmetric multi-bolted connection. The normal loading and unloading direction of the contact joint was considered. The tests were performed with the use of an INSTRON 8850 servo-hydraulic testing machine equipped with an extensometer. A normal stiffness characteristic in the form of an exponential function was proposed for the tested contact joint. It will be applied in the second part of the paper, in which finite element modelling of the multi-bolted connection will be presented.