The invention is to provide a catalyst for long-term, high-yield and stable production of ethylene and propylene in an efficient and simple method of catalytic conversion from a hydrocarbon material. The invention relates to a method for producing ethylene and propylene by contacting a hydrocarbon material that contains an olefin having from 4 to 12 carbon atoms in an amount of at least 20% by weight, with a zeolite-containing shaped catalyst satisfying the following requirements (1) to (4), in a reactor for catalytic conversion of that olefin: (1) the zeolite is an intermediate pore-size zeolite having a pore size of from 5 to 6.5 angstroms, (2) the zeolite does not substantially contain a proton, (3) the zeolite contains at least one metal selected from the group consisting of metals belonging to the Group IB of the Periodic Table, (4) the zeolite has a silica/alumina molar ratio (SiO2/Al2O3 molar ratio) of from 800 to 2,000.