We compute analytic expressions for the nonlinear optical response functions for the Peierls model of a conducting polymer by using the Keldysh non-equilibrium Green's function methods. The only parameter in the model is the gap, which can be determined independently from the linear optical response. Our results for 3rd harmonic generation are in excellent agreement with experiments on polyacetylene. This constitutes strong evidence that polyacetylene is well described by a model of weakly interacting quasi-particles. Further nonlinear optical effects, which should be experimentally observable, are predicted.