Extrusion method and apparatus in which the liquid precursor of the extruded material is forced through a die formed by two surfaces moving in opposite directions relative to one another and transversely to the direction of material flow. Immediately upon exiting this dynamic die, the extracted material is removed as a sheet or film through a take-off system. In a preferred embodiment of the invention, the first die is formed by members rotating on a common axis in opposite rotational directions.