An unbounded parallel flow, consisting of a linear shear layer between uniform streams, is investigated for stability. A conventional eigenvalue problem is formulated, and solved by both analytical and numerical methods. The region of instability in the plane of Reynolds number R and disturbance wave number α is determined, and typical growth rates in the unstable region are computed.Unstable disturbances are found at all values of R. Results for αR > 100 are found to agree closely with inviscid theory results. An analytic method useful for αR < 1 is developed.The extent to which the present results can be applied to the laminar boundary layer between free streams is discussed.