Solar chimneys are often used to extract air from a building by thermal stacks, while subfloor plenums are used to passively cool air before it is supplied to a building. This paper examines the overall flow pattern in buildings with both solar chimneys and subfloor plenums. For a multi-zone flow system in which each zone has only two effective openings, an analytical solution is derived. A sufficient condition for upward flows to occur is derived from the analytical solution.