Abstract: The invention relates to a process for the production of mould-foamed poly(meth)acrylimide (P(M)I) cores, in particular of polymethacrylimide (PMI) cores, which can be used by way of example in automobile construction or aircraft construction. A feature of this process is that polymer granules or polymer powder are charged to a compression mould where they are foamed. A particular feature of the process is that said two-shell compression mould has, respectively on both sides, a cavity that conforms to the shape and which serves for both the heating and the cooling of the granules and, respectively, of the rigid foam core produced therefrom.