AbstractA method of analysis is presented for two structures which have connections with clearance. It is assumed that the behaviour of the structures is described, by the movement of discrete nodes and that as the load on the structure changes, clearances open or close between corresponding nodes on the structures; each time this occurs the stiffness of the combined structure changes because its configuration has changed. Between these changes, the structure will behave linearly and the overall behaviour can be described as piecewise linear. Applications include diesel engine crankshafts with bearing clearances and the wrap‐around problem in pin‐and‐eye connec