Abstract: A method for producing a casting mould for filling with melt and/or a core for producing a hollow space in a cast part, includes forming a wall made of a refractory and gas-permeable material. The wall is formed to include an inner wall and a support structure built up in successive layers against the inner wall. The inner wall is formed with an inner surface defining a roughness matching the surface roughness of the part that is to be cast in the mould. A generative manufacturing method generates the successive layers of the support structure, which includes open and/or closed hollow spaces and/or different thicknesses of the successive layers of the support structure that supports the casting mould independently against the casting pressure in a dimensionally stable manner and also isolates or dissipates thermal energy in the melt in a targeted manner.