The flow of thin viscous films over complex surfaces is relevant to the description of heat and mass transfer processes in ordered packing materials. Ordered packings, usually made of corrugated sheets of metal, plastic or ceramic materials have important operating advantages and usually outperform random packings of similar characteristics. A two-dimensional streamline function is used to compute the components of the velocity field and to reduce the equations of motion to a single, nonlinear, ordinary differential equation for the film thickness. A perturbation solution for small film thickness is developed that predicts two film surface maxima for each cycle of the solid surface. Normal film thickness profiles are measured in a direction normal to the solid surface, as opposed to experimental film thickness measured in a direction normal to the axis of the solid surface. The agreement between experimental and theoretical normal film thickness is very good for small values of the parameter delta, defined as the ratio of the Nusselt film thickness and the amplitude of the wavy solid surface.