The hydrodynamics of oil slick containment are examined. It is shown that containment is only possible when a densimetric Froude number based on flow velocity and depth and the oil density is less than a critical value. Experiments confirmed that an oil slick was unable to maintain a stationary front when the Froude number exceeded the critical value. It is also shown that viscous effects ultimately limit the thickness and therefore the length and volume of any real slick. Expressions are derived which enable these limits to be determined.