A recent model of the behavior of Gaussian chains in steady shear flow [J. Chem. Phys. 112, 8707 (2000)] is extended to include the effects of stiffness and finite extensibility. Calculations of the shear rate dependence of fractional elongation and of the time dependence of size fluctuations are found to be in good agreement with results from an experimental study of the behavior of single chains of DNA in steady shear flow. As in the earlier approach to the polymer-flow problem, we have ignored excluded volume and hydrodynamic interactions, but have instead added a bending energy contribution to the Hamiltonian of the chain, and have treated the usual connectivity term as a contribution to chain stretching that can be adjusted to ensure that the average size of the chain is fixed. The inclusion of stiffness and finite extensibility in the present treatment is found to produce significant improvements over the approach based purely on flexible chains.