Loss factors for vibrating plates made of a vibration damping steel sheet (VDSS), which is constructed at three layers with a viscoelastic resin core, are predicted by the finite-element method. Basic equations of the finite-element dynamic analysis for the VDSS are presented. The complex stiffness matrix results from the complex elastic constant of the core resin, and complexeigen values for the whole system give was modal loss factors and damped modal frequencies. Numerical calculation for rectangular plates excited at the center of plates are performed. Compliance curves at the excited point of plates with various aspect ratios are obtained and loss factors are estimated by the hal-value bandwidth of the 1st and 2nd peaks of compliance curves.