Finite element modelling of multi-bolted foundation connections used for the foundation of heavy machinery or equipment is presented. Connections made using different types of shims, with particular emphasis on polymer–steel shims, are investigated. The stiffness characteristics for the adopted models of multi-bolted foundation connections at the installation stage are described and compared. It is shown that the use of polymer–steel shims can result in a significant improvement in the stiffness of a multi-bolted foundation connection compared to a connection with a polymer shim, and in achieving a multi-bolted foundation connection with a stiffness similar to that of a connection with a steel shim (at a sufficiently low polymer layer thickness).