We will consider boundary value problems of elastic systems presenting singular behavior in the bulk and on the boundary. Two types of constitutive equations of elastomers will be addressed: isotropic and nematic liquid crystals. In the former, we will study slender domains subject to large strain, that cause loss of hyperelasticity of the material. In the second case, the appearence of isotropic liquid crystal defects follows as a result of the nonconvexity of the free energy of the elastomer.