We study the stability of plane Poiseuille flow of two immiscible liquids of different viscosities and equal densities. The problem is like one considered by C. S. Yih who found that flow in two layers of equal thickness was always unstable. We find regions of stability when there are three layers with one of the fluids centrally located. We view our contribution as a study of selection of stable steady flow from a nonunique continuum of Poiseuille flows all of which satisfy the steady Navier-Stokes and which differ from another in the number and thickness of layers of different viscosity. Experiments have shown that there is a tendency for the less viscous fluid to encapsulate the more viscous one. This arrangement of components, with the more viscous fluid in the center of the channel maximizes the mass flux for a fixed pressure gradient. A linear stability analysis of centrally located configuration to long waves is carried out by the analytic methods introduced by Yih [1]. The stability results depend on the viscosity and volume ratio in a fairly complicated way. The flow with the high viscosity fluid centrally located is always stable. Centrally located layers of less viscous fluid, called fingering flows, are always unstable.