Theoretically, the rate of capillary penetration of a polymer melt into a slit, a model for a surface irregularity, has been shown to depend on γcosθ/η) where γ refers to the surface tension of the liquid, η its viscosity and θ a time-dependent contact angle. Analytical expressions relating the depth of penetration with time have been experimentally verified by observations of the penetration of molten polyethylene and poly-(ethylene-vinyl acetate) into aluminum channels. Values of η, calculated from the observed data, agree closely with independent determinations of this material parameter. A theoretical treatment has also been developed which describes the velocity of spreading of a liquid drop over a flat surface. Flow equations for the flow of free films were adapted for this purpose. The spreading velocity is predicted to depend on the product of three factors (1) a scaling factor, (γ/η1Ro), where Ro is the initial radius of curvature, (2) cosθ∞. (l-cosθ/cosθ∞) where θ∞ refers to the equilibrium value of θ, and (3) geometric terms. After demonstrating that a drop of molten polymer may be treated as a spherical cap, the predicted dependence of spreading rate on drop size, cosθ∞ (nature of the substrate) and the scaling factor was experimentally verified. Some discrepancies noted at long times and high temperatures are discussed. © 1969 Taylor & Francis Group, LLC. All rights reserved.