Feasibility studies on planar millimeter-wave cavity structures have been made. The structures could be used for linear accelerators, free-electron lasers, mm-wave amplifiers, or mm-wave undulators. The cavity structures are intended to be manufactured by using DXL (deep x-ray lithography) microfabrication technology. The frequency of operation can be about 30 GHz to 300 GHz. For most applications, a complete structure consists of two identical planar half structures put together face-to-face. Construction and properties of the constant gradient structures that have been investigated so far will be discussed. These cavity structures have been designed for 120 GHz 2π/3-mode operation.