Strain-energy density functions (W) of end-linked polydimethylsiloxane (PDMS) networks with different entanglement densities were estimated as a function of the first and second invariants I-1 and I-2 of Green's deformation tensor on the basis of the quasi-equilibrium biaxial stress-strain data. Entanglement densities in the PDMS networks were controlled by varying the precursor PDMS concentration ((,) in end-linking. The deduced functional form of W [W = C-10(I-1 -3) + C-01(I-2 - 3) + C-11(I-1 - 3)(I-2 - 3) + C-20(I-1 - 3P + C-02(I-2 - 3)(2)] is independent of the degree of dilution at network preparation. The contribution of each term in I-1 and I-2 to total energy depends on whether the precursor PDMS solution before end-linking belongs to the concentrated regime phi(0) > phi(c) where many entanglement couplings of precursor chains exist or the moderately concentrated regime phi(0) < phi(c) where pronounced entanglement couplings of precursor chains are absent. These results suggest that the rubber elasticity of the end-linked networks is significantly influenced by the entangled state of precursor chains before end-linking, and the extra terms in the estimated W that are absent in the prediction of the classical rubber elasticity theories [W = C (I-1 - 3)] mainly originate from the effect of trapped entanglements.