Non-compression (NC) braces resist only a tensile axial force. A frame with Z-type NC braces deform in a single side of direction under a cyclic ground motion. An analytical study on frames with Z-type NC braces was carried out to clarify deformation behavior of the rigid frames. The following conclusions were obtained from the analytical results: 1) Multi-story frames with same-directional Z-type braces deform in a single direction under seismic ground motions. 2) Frames with alternate Z-type braces deform in small top displacement because of multi-degrees of deformation under earthquakes.