A silver catalyst for the direct oxidation of ethylene with oxygen to give ethylene oxide is applied on a porous carrier and essentially consists of .alpha.-alumina and contains certain amounts of soluble calcium, aluminum, potassium and sodium salts. The carrier has a BET surface area of from 0.2 to 0.8 m.sup.2 /g, a pore volume of not less than 0.5 ml/g, the pores being equally accessible to cold and warm water, and a bulk density of less than 650 kg/m.sup.3, and has a shape which, in the reactor, provides a geometric surface area of not less than 600 m.sup.2 /m.sup.3, on which more than 13% by weight of silver are applied as the active component, more than 110 kg of silver being available per m.sup.3 of reactor.