This paper presents analytical modeling of disk-type Variable Friction Tactile Displays (VFTD) producing squeeze-film air damping elicited by ultrasonic flexural standing waves of piezoelectric-glass composites. Energy-based Lagrangian mechanics was employed to derive the system dynamic equations of motion of the VFTD vibrating at its fundamental mode. The coefficient of mode shape function and the accumulated electric charge on a piezoelectric element were adopted as two generalized coordinates for the Lagrangian formulation. The derived analytical models can predict undamped free and forced vibrations of VFTDs with hinged or clamped edges. The issues of open-circuit and short-circuit fundamental frequencies and the electromechanical coupling coefficients for several VFTDs with different dimensions were discussed for the optimal design of vibration-induced tactile displays. The theoretical fundamental frequencies were compared with experimental results for the verification of the proposed analytical model.