Pneumatic tires conception relies on balancing traction, handling, wear, rolling resistance, and aggression resistance, for which various rubber constitutive and fracture models have been developed. Their industrial use needs robust models and databases, and numerical techniques able to deal with large strains and stiff problems. Practical issues raised by these calculations will be remembered, and some examples given. Microsphere models allow to relate observed macroscopic behaviour to material mechanisms. A toy model will illustrate cyclic softening.