Conventional guest-host optical limiting materials utilize either a liquid solvent or solid as the matrix for nonlinear absorbing chromophore dopants. Concentration gradients of the chromophore in the matrix can improve optical limiting performance. However, low viscosity liquid solutions can not retain a concentration gradient while polymer solid matrices damage at low laser fluences. We report on a novel approach of using an elastic polymer (an optical epoxy) and viscoelastic gels for guest-host optical limiting matrices. We achieve high bulk laser damage thresholds in the hosts and maintain a concentration gradient of the chromophore. By softening the epoxy we significantly enhance it's bulk laser damage threshold. We characterize this effect by measuring the damage threshold as a function of viscoelastic properties (shear modulus and glass transition temperature). In addition, optical limiting was demonstrated in all the hosts doped with nonlinear phthalocyanine chromophores.