The linear stability of plane three_layer vertical Poiseuille flow is considered. The layers are composed of two immiscible fluids, one next to the walls and one centrally located. The fluids have different viscosities and densities and surface tension effects are included. Intuitively, an analogy with the concentric Hagen-Poiseuille flow is expected and the similarities and differences are investigated. The ability of heuristic reasoning to predict which arrangements are more likely to be observed is tested. Numerical results concerning low Reynolds numbers, as well as the behavior of eigenvalues close to the first criticality of the one_fluid problem, are presented.