In this paper the multiperiod planning and scheduling of multiproduct plants under demand uncertainty is addressed. The proposed stochastic model, allowing for uncertain product demand correlations, is an extension of the deterministic model introduced by Birewar and Grossmann (Ind, Eng, Chem, Res. 1990, 29, 570). The stochastic model involves the maximization of the expected profit subject to the satisfaction of single or multiple product demands with prespecified probability levels (chance-constraints). The stochastic elements of the model are expressed with equivalent deterministic farms, eliminating the need for discretization or sampling techniques. This implies that problems with a large number of possibly correlated uncertain product demand can be efficiently handled. The resulting equivalent deterministic optimization models are MINLP’s with convex continuous parts. An example problem involving 20 correlated uncertain product demands is addressed. A sequence of different models is considered which highlight different modeling features and their effect an computational performance and obtained results.