Abstract: In the thermal cracking of a heavy petroleum oil (having an API specific gravity of not more than 25) in a tubular type heating furnace, possible occurrence of coking trouble inside the furnace can be prevented by applying a magnetic field of fixed magnitude transversely to the flow of the heavy petroleum oil being introduced into the furnace or by applying a fixed magnitude of magnetic field transversely and, at the same time, applying a fixed magnitude of direct-current voltage parallel to the flow of the heavy petroleum oil being introduced into the furnace. More effective prevention of occurrence of coking can be obtained by having a specific inorganic substance incorporated in the heavy petroleum oil before the oil is subjected to the magnetic field or to simultaneous application of the magnetic field and voltage.