We consider several problems in which two phases of matter flow through each other. In all of these problems, the motion of the two phases is described as if each were a continuum. We shall be concerned with the development in simple flows of instabilities produced by gravity through the Archimedes force. As a result of this instability, there is a tendency for the phases to separate and produce significant horizontal inhomogenities. The examples are Benard convection, bioconvection, fluidized beds, and the flow of radiation through matter. Each can be viewed as an instance of Archimedean instability in a two-phase continuum.