We present a finite chain-length calculation of the rubber elasticity of an isotropic crosslinked network of freely jointed chains under affine deformation. Whilst this is a classical calculation, the result is derived in its full tensorial structure for the first time, and new predictions of non-Gaussian elasticity for general biaxial deformations are presented. The full tensorial rubber-elasticity derivation allows any deformation regime to be treated, to facilitate validation with experimental data. Even though more complex many-chain effects are neglected, this theory appears to be the only one to offer a physical explanation for negative values of W-2 observed experimentally at small strains.