Low speed and high speed flow phenomena in pillow plate channels are considered. High speed flows were investigated by means of analytical methods and fully three-dimensional computational fluid dynamics (CFD) simulations. The theoretical analysis indicated that a Fanno-type flow model described high speed flow behavior in pillow plate channels reasonably well. Since only wavy walls with smooth profiles were involved, linearized gas dynamics was applied in order to derive similarity laws for the high speed flows. The detailed CFD analysis was used to support the assumption of a Fanno-type flow. The effects of the wavy wall structures on pressure drop and Mach number distribution within the flow path were investigated in detail. The present analysis demonstrates that pillow plate heat exchangers represent promising candidates for high speed turbo machinery applications.