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The theory of rubber elasticity is reformulated on the basis of a statistical distribution of the end-to-end distance partially accounting for intramolecular ecluded volume. The relationship between the uniaxial stress, $\sigma$, and the elongation ratio, $\alpha$, is: $$\sigma =\frac{5}{3}\nu kT\left(\alpha -\frac{1}{{\alpha }^2}\right)-\nu kT\mathrm{\Phi }(\alpha )$$ where $\nu$ is the number of effective chains per unit volume, and $\mathrm{\Phi }(\alpha )$ is a function with a maximum close to $\alpha =2,5$. The elastic modulus for $\alpha =1$ turns out to be 1.27 times the value calculated by the classical Gaussian theory.