The invention relates to a process for the production of mold-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 preheated under pressure are moreover charged under pressure to a compression mold where they are foamed with depressurization. In particular, a feature of the process is that it optionally uses a preferably two-shell compression mold for the heating and also for the cooling of the granules and, respectively, the rigid foam core formed therefrom.