RF-dipole crabbing cavities are being considered for a variety of crabbing applications. Some of the applications are the crabbing cavity systems for LHC High Luminosity Upgrade and the proposed Electron-Ion Collider for Jefferson Lab. The design requirements in the current applications require the cavities to incorporate complex damping schemes to suppress the higher order modes that may be excited by the high intensity proton or electron beams traversing through the cavities. The number of cavities required to achieve the desired high transverse voltage, and the complexity in the cavity geometries also contributes to the wakefields generated by beams. This paper characterizes the wakefield analysis for single cell and multi-cell rf-dipole cavities
