Method for producing plate- and/or shell-like components which have a singly or doubly curved, in particular cylindrically and/or dome-like curved and/or arched and/or free shape, wherein a curable raw material which has a substantially slurry-like pasty consistency and is based on a mixture of at least one binder comprising fibrous components is applied to an outer surface of an inner mould made of a material which is substantially impenetrable to at least said raw material, said outer surface designed corresponding to the shape of the components, and is left to cure there, characterised in that - a mixture of a binder comprising at least 35 wt.% of fibres and/or fibre-containing particles, based in each case on the mixture as a whole, said mixture comprising a density of less than 1.2 t/m 3 in the dried state, is applied as a raw material to the entire outer surface of the inner mould or at least to sub-regions- of same, - that a fluid-tight or gas-tight outer shell or outer film is applied to the entire outer surface of the open-pore or open-cell binder/fibre and raw material mixture comprising air inclusions and air bubbles or at least to sub-regions of same so as to have planar contact with or rest in a planar manner on said outer surface, - that said outer shell is connected to the outer surface of the inner mould or to the inner mould in each case on the edge (1") thereof in a substantially fluid-tight or gas-tight manner, and - that an absolute pressure of less than 0.7 bar is produced in an intermediate space via at least one suction connection point connected to said intermediate space between the outer shell and the outer surface (1', 2') of the inner mould or of the binder/fibre and raw material mixture applied to said outer surface, - until the binder/fibre mixture or raw material has begun to cure in a predominantly dimensionally stable and self-supporting manner at least in the region of the outer surface thereof, - after which the resulting component and at least the inner mould are separated from each other or not. - a mixture of a binder comprising at least 35 wt.% of fibres and/or fibre-containing particles, based in each case on the mixture as a whole, said mixture comprising a density of less than 1.2 t/m 3 in the dried state, is applied as a raw material to the entire outer surface of the inner mould or at least to sub-regions- of same, - that a fluid-tight or gas-tight outer shell or outer film is applied to the entire outer surface of the open-pore or open-cell binder/fibre and raw material mixture comprising air inclusions and air bubbles or at least to sub-regions of same so as to have planar contact with or rest in a planar manner on said outer surface, - that said outer shell is connected to the outer surface of the inner mould or to the inner mould in each case on the edge (1") thereof in a substantially fluid-tight or gas-tight manner, and - that an absolute pressure of less than 0.7 bar is produced in an intermediate space via at least one suction connection point connected to said intermediate space between the outer shell and the outer surface (1', 2') of the inner mould or of the binder/fibre and raw material mixture applied to said outer surface, - until the binder/fibre mixture or raw material has begun to cure in a predominantly dimensionally stable and self-supporting manner at least in the region of the outer surface thereof, - after which the resulting component and at least the inner mould are separated from each other or not.