The development of the statistical theory of rubber elasticity in the 1940s followed by finite strain elasticity theory in the 1950s and of convenient forms for the strain energy function in the 1970s focused rubber research on modelling the elastic characteristics of rubber. Extensive literature has appeared since then which seeks to expand this area. Even so, the Physics of Rubber Elasticity by L.R.G. Treloar 1 first published as an updated 3rd edition in 1975 still remains the most valuable review of the fundamental principles. The treatment of rubber as a 'hyperelastic' material, whose behaviour is modelled by a strain-energy function for finite strains, was implemented into finite strain element analysis packages in the 1980s and is now widely available in several commercial software packages. Experienced engineers working in the rubber design or research arena soon realised that only a few engineering elastomers, such as unfilled natural rubber, can be modelled reliably using this type of ideal 'hyperelastic' behaviour. Most other engineering elastomers incorporate 'reinforcing' fillers, in order to improve strength properties, to improve processing characteristics or to change the modulus of the material. The stress-strain characteristics of such filled elastomers depart significantly from the simplest elastic models. With dramatic increases available in complexity now possible due to the advancement in computer systems there has been an opportunity for more than the last decade to develop and apply much more sophisticated models to tackle other aspects of inelastic behaviour that are of practical interest to engineers. This has two possible benefits; firstly to allow models to be developed that are implementable in finite element analysis to predict the behaviour and secondly to develop a better understanding of the physical phenomenon at a molecular level in elastomer materials that give rise to these effects.