Case II diffusion of penetrant liquids in polymer films is characterized by constant-velocity propagation of a phase interface. We review the development of viscoelastic models describing case II diffusion and then present a phase plane analysis for traveling wave solutions. For simplified, piecewise-constant coefficient models we give closed-form analytic solutions showing the dependence on various physical parameters in both viscous and viscoelastic diffusive systems. We will also compare the results of our analysis with results from numerical simulations of more general models.