•A geometrical model of a continuously scanning laser vibrometer is built.•Continuously and synchronously scanning relations among three vibrometers are established.•Vibration measurement of a beam and plate is conducted by a 3D continuous scanning system. This paper presents for the first time an investigation of three-dimensional (3D) vibration measurement by three scanning laser Doppler vibrometers (SLDVs) in a continuously and synchronously scanning mode. Three laser spots from the three SLDVs continuously move along the same scan trajectory and synchronously measure vibration of the same point on a surface of a structure. The three SLDVs, i.e., Top, Left, and Right SLDVs, are from a Polytec PSV-500-3D system and input signals to scan mirrors of each SLDV are controlled by an external dSPACE MicroLabBox control unit. The whole system is called a 3D continuously SLDV (3D-CSLDV) system. Methodologies are developed in this investigation to achieve the continuously and synchronously scanning mode by the system. First, the geometrical model of a CSLDV is built to obtain locations of the three CSLDVs with respect to a specified measurement coordinate system (MCS). Second, a scan trajectory on the measured surface is defined and rotation angles of scan mirrors of the Top CSLDV are obtained by scanning the trajectory. Third, since locations of the three CSLDVs with respect to the MCS have been obtained in the first step, rotation angles of scan mirrors of Left and Right CSLDVs to scan the defined trajectory can be obtained from those of the Top CSLDV based on spatial relations among the three CSLDVs. Experiments to scan a beam and a plate were conducted using the 3D-CSLDV system. Operating deflection shapes (ODSs) of the beam and plate in three directions of the MCS were obtained and they were in good agreement with those obtained by traditional step scanning. The results demonstrate the feasibility of 3D vibration measurement by the 3D-CSLDV system in a continuously and synchronously scanning mode.