The Frank elastic constants of lyotropic polymer liquid crystals are formulated using an equivalent freely-jointed chain model, which can be uniquely defined by the parameters of the corresponding wormlike chain and the polymer concentration. The contribution of the higher virial terms to the elastic constants was taken into account on the basis of the scaled particle theory used previously for undistorted nematic polymer solutions. The fomulated elastic constants are applicable to systems with any polymer conformation from the rod limit to the coil limit and at arbitrary concentration and degree of orientation. The theoretical elastic constants for twist and bend distortions agree semiquantitatively with most experimental results for the elastic constants of lyotropic liquid crystals of poly(gamma-benzyl glutamate) with no adjustable parameters.