A method of casting a component (42) having convoluted interior passageways (44). A desired three dimensional structure corresponding to a later-formed metal alloy component is formed by stacking a plurality of sheets (18, 20) of a fugitive material. The sheets contain void areas (22) corresponding to a desired interior passageway in the metal alloy component. A ceramic slurry material is cast into the three dimensional structure to form either a ceramic core (34) or a complete ceramic casting vessel (38). If just a ceramic core is formed, a wax pattern is formed around the ceramic core and an exterior ceramic shell (38) is formed around the wax pattern by a dipping process prior to the removal of the fugitive material and wax. An alloy component having the desired interior passageway is cast into the casting vessel after the fugitive material is removed.