A new formula for the force vs extension relation is derived from the discrete version of the so-called wormlike chain model. This formula correctly fits some recent experimental data on polymer stretching and some numerical simulations with pairwise repulsive potentials. For a more realistic Lennard-Jones potential the agreement with simulations is found to be good when the temperature is above the 0 temperature. For lower temperatures a plateau emerges, as predicted by some recent experimental and theoretical results, and our formula gives good results only in the high force regime. We briefly discuss how other kinds of self-interactions are expected to affect the elasticity of the polymer.