In this paper, we address the problem of designing flexible plant layouts for manufacturing facilities where product demands are subject to variability. A flexible layout is one that maintains low material handling costs despite fluctuations in the product demand levels. We extend existing procedures for design of flexible layouts by (1) explicitly capturing the stochastic nature of product demands and the resulting variability in material flows between different processing departments, (2) allowing for the possibility of multiple processing departments of the same type to exist in the same facility, and (3) letting material flows between pairs of individual departments be determined simultaneously with the layout and as a function of demand scenarios. Optimal and heuristic methods are presented for generating flexible layouts and determining flow allocations under various design and operation assumptions.