We present a model calculation of the elasticity of a nematic elastomer of finite-length network strands under affine deformation. The result is derived in its full tensorial structure, and its predictions are examined. In particular, we look at the non-Gaussian corrections to the effects of soft elasticity and elastic anisotropy. We find that the soft modes can at most be hardened at O(N-2) when compared to the conventional rubber elastic energy, where N is the number of monomer units along a typical strand. The elastic moduli for extensions parallel and perpendicular to the nematic director are found to differ at O(N-1).