Deformation of Earth's crust and lithosphere is characterised by elastic, viscous and brittle material behaviour. The implementation of this complex rheology is a challenge for numerical models owing to variations in laboratory and natural data, the choice of equations to describe the deformation processes and the different flavours of their numerical representation. I discuss some of the current issues associated with the role of elasticity in crust- to lithosphere-scale processes, the implementation of brittle behaviour in continuum models and the use of laboratory viscous flow laws. Results of numerical models show that the style of lithosphere deformation is strongly influenced by strength contrasts between materials. Numerical models can be used to evaluate the role of such strength contrasts and of the individual rheological components by testing model sensitivity to variations in parameter values.

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