Elasticity is measured on a stress-strain diagram. 

Stress is applied to a material sample and the resulting strain (deformation) is measured. 

In the limit of small to nominal stresses, the slope of the resulting stress-strain curve is linear and the relationship is characterized by the modulus of elasticity (E): strain = E * (applied stress) 

An important property of the elastic response is that when the applied stress is removed, the sample returns to its undeformed state. 

However, in the limit of large applied stress, the curve stops being linear, and the material starts to demonstrate plastic deformations (permanent deformation to the material.) 

If your sample of rubber is less elastic than the steel, it simply means that at the same level of large stress, the rubber enters the plastic limit while the steel remains within its elastic limit. that means the same stress causes plastic deformations in the rubber sample while the steel sample returns to the no-stress configuration. 

That's how steel can be more elastic than rubber.

Hope this helps:)