This thesis is concerned with the characterization of layered contact problems. The research project has been prompted by an investigation into creep, and ultimately, gross sliding, of rubber tyres fitted around steel wheels in earth moving equipment. In general, slippage between tyre and rim is experienced in common engineering applications employing tyred systems. A general and systematic approach for investigating the interfacial behaviour of tyred systems has consequently been proposed. Classical techniques together with novel numerical approaches based on advanced mathematical programming have been implemented to support the investigation. Creep between mating surfaces, frictional shakedown and measuring friction in partial slip condition are the main objects of investigation. The analytical and numerical models developed by the author have been complemented by experimental work, whose detailed description is also included in this thesis. Finally, further studies have been performed to shed light on some of the design issues offered by the threedimensional full-scale engineering application. The numerical approach based on finite element modelling used to tackle these aspects of the project and the experimental work carried out by the author to corroborate the numerical findings are also presented.