The flow of thin viscous films over complex surfaces is relevant to the description of heat-and mass-transfer processes over ordered packings. This work focuses on the gravity-induced bulk spreading of a liquid point source over periodic surfaces. This simulates the flow from a drip point over ordered packings in packed beds. Experimental observations indicate that in the absence of contact lines, for corrugations normal to the vertical, the liquid film adopts a shape similar to a Gaussian distribution as it spreads down the solid surface. For this type of flow, a viscous long-wave-type approximation was used to derive a film evolution equation. The film evolution equation retains all three possible driving forces, i.e., components of gravity normal and tangent to the solid surface and capillarity. Agreement between experimental and predicted film thicknesses is seen to be quite good. Experimental data are given also on flow over complex surfaces with corrugations inclined with respect to the vertical.