This study treats wave motion within rectangular and sloping rockfill embankments with impervious cores. The non-Darcy flow in the rockfill is solved by a finite difference one-dimensional model. The characteristic directions are used to control the discretization of the solution domain. The entrance boundary condition (outcrop point) is computed from the external wave motion on the face of the rockfill. An equivalent rectangular section is used to approximate a sloping embankment, and waves on slopes are classified as 'fast' or 'slow rising.' The mathematical model yields phreatic line profiles with time. The model is supported by several wave flume experiments.