  Uniaxial elastomers are characterized by five elastic constants. If their
elastic modulus C_5 describing the energy of shear strains in planes containing
the anisotropy axis vanishes, they are said to be soft. In spatial dimensions d
less than or equal to 3, soft elastomers exhibit anomalous elasticity with
certain length-scale dependent bending moduli that diverge and shear moduli
that vanish at large length-scales. Using renormalized field theory at d = 3
and to first order in \epsilon = 3 - d, we calculate critical exponents and
other properties characterizing the anomalous elasticity of two soft systems:
(i) nematic elastomers in which softness is a manifestation of a Goldstone mode
induced by the spontaneous symmetry breaking associated with a transition from
an isotropic state to a nematic state and (ii) a particular version of what we
call a critically soft elastomer in which C_5 = 0 corresponds to a critical
point terminating the stability regime of a uniaxial elastomer with C_5 > 0.
