Two-fluid models of cosmic-ray modified radiative shocks were constructed for the purpose of interpreting optical emission from astrophysical shocks, including shocks in supernova remnants. The structure and stability of cosmic-ray modified radiative shocks without additional source terms were investigated first. Such a shock differs from a radiative shock that does not co~tain cosmic rays in that a cold dense layer does not fo\-m and the radiative overstability is always suppressed. If the diffusion length is comparable to or greater than the cooling length, the shock is nearly isothermal. Steady shocks exhibit efficient conversion of shock kinetic energy into cosmic ray energy, and multiple .shock solutions for a given d.istant upstream state, which exist for adiabatic cosmic-ray modified shocks, were not found. When source terms are included that transfer energy from the cosmic-ray component to the thermal component due to an acoustic instability that may occur in a cosmic ray precursor, some properties of °radiative shocks and adiabatic cosmic-ray modified shocks, respectively, are recovered. A cold dense layer forms and the thermal overstability of radiative shocks occurs if the coupling is sufficiently strong. The acceleration efficiency of solutions depends on the strength of coupling, and multiple solutions exist for some shock parameters. A Balmer dominatE(d filament (knot g) in Tycho's supernova remnant provides a test for adiabatic cosmic-ray modified shock models. A model of a shock in a transient state that satisfies some constraints derived from Balmer line spectra was found, but the shock model does not reproduce the observed Ha emissivity profile. Finally, non-equilibrium-ionization cooling was introduced, and the resulting shock models are suitable for shock diagnostic studies.