The invention relates to an oxidation catalyst comprising at least one inorganic, oxidic or ceramic, shaped support body having a BET surface area of less than 0.5 m2/g, based on the support, which is at least partly coated with a catalytically active multielement oxide, the catalyst being precious metal-free and the shaped support body having the form of a saddle whose saddle surface is curved oppositely in the two principal directions, to a process for producing it, to its use in various catalytic gas phase oxidations, and to corresponding processes for catalytic gas phase oxidation.