  We develop a novel biased Monte-Carlo simulation technique to measure the
force-extension curves and the distribution function of the extension of
fluctuating filaments stretched by external force. The method is applicable for
arbitrary ratio of the persistence length to the contour length and for
arbitrary forces. The simulation results agree with analytic expressions for
the force-extension curves and for the renormalized length-scale-dependent
elastic moduli, derived in the rigid rod and in the strong force limits. We
find that orientational fluctuations and wall effects produce non-Gaussian
distributions for nearly rigid filaments in the small to intermediate force
regime. We compare our results to the predictions of previous investigators and
propose new experiments on nearly rigid rods such as actin filaments.
