Polymeric nematic liquid crystals crosslinked into elastomers (solid l
iquid crystals) are shown to display novel and complex elasticity. The
internal (nematic) direction can experience a barrier to its rotation
which couples to standard elasticity. We predict a new phenomena uniq
ue to anisotropic rubber - a ''soft elastic response''; uniaxial strai
n is developed without resistance below a critical deformation lambda
due to the relaxation of related shear strains and reorientation of t
he nematic director. We discuss possible experiments to verify this pr
ediction and interpret the existing experimental observation in terms
of the concept of ''soft elasticity''.