A model suitable for simulating lyotropic polymer liquid crystals (PLCs) is described. By varying the persistence length between infinity and 25, the effect of increasing flexibility on the nematic-smectic transition of a PLC with a length-to-width ratio L/D= 6 is investigated. It is found that increasing flexibility shifts the formation of a smectic phase to higher densities. Comparison is made with a recent theory of the nematic-smectic transition of slightly flexible rods.