We study multiple muon events (muon bundles) recorded underground at a depth of 2090 mwe. To penetrate to this depth, the muons must have energies above 0.8 TeV at the Earth`s surface; the primary cosmic ray nuclei which give rise to the observed muon bundles have energies at incidence upon the upper atmosphere of 10 to 10{sup 5}TeV. The events are detected using the Soudan 2 experiment`s fine grained tracking calorimeter which is surrounded by a 14 m {times}10 m {times} 31 m proportional tube array (the ``active shield``). Muon bundles which have at least one muon traversing the calorimeter, are reconstructed using tracks in the calorimeter together with hit patterns in the proportional tube shield. All ionization pulses are required to be coincident within 3 microseconds. A goal of this study is to investigate the relative nuclear abundances in the primary cosmic radiation around the ``knee`` region (10{sup 3} {minus} 10{sup 4} TeV) of the incident energy spectrum. Four models for the nuclear composition of cosmic rays are considered: The Linsley model, the Constant Mass Composition model (CMC), the Maryland model and the Proton-poor model. A Monte Carlo which incorporates one model at a time is used to simulate …