We have developed a new spring force law which can be used in bead-spring chain models of the worm-like chain. The bead-spring chain has no bending potentials between the springs, and so differs from the current models only in the functional form of the force law. This new model can accurately represent a chain that contains many persistence lengths even if each spring represents only a few persistence lengths. We also discuss the assumptions in the model and other sources of possible error. The new force law significantly reduces the error compared with using the Marko-Siggia interpolation formula. (c) 2006 The Society of Rheology.