The calculus of variations is applied to the analy- sis of the short-circuit resonant properties of piezoelectric vib- rators. A stationary expression is derived from the equations of motion for such vibrations. This stationary expression is used to develop a approximation technique for detennin- ing the short-circuit resonant frequencies and the corresponding mechanical displacements and electric potentials. The technique is used to analyze the short-circuit resonant properties of fully electroded piezoelectric ceramic discs with comparable diameter and thickness dimensions. Agreement of the barium titanate resonant frequency calculations with Shaw's published experimental frequency spectrum is better than three percent for the lowest eight resonances. Also, exact solutions have been obtained for the equivoluminal modes supported in isotropic elastic discs of certain diameter-to-thickness ratios. The application of the elastic portion of the present electroelastic approxi- mation to such discs produced frequency values for these modes which agree with the exact values to better than 0.3 percent. In the present paper, a stmatiormy expression describing the steady-state vihrations of n piezoelectric insulat,ing solid with N short-circuit,ed clectrodcs on its surface is derived from the steady-stale equations of motion. The stat'iorltlry property of this cspression is used to develop a variational approsirnation technjque for short-c-ircuit elec- troelastic vibration anxlyscs. The technique is applied to the short-circuit vibrations of fully-electroded piczoelec- tric ceramic discs mit.11 comparable diameter and thickness dimensions. Agreeenlent between the BaTi03 calculations and Slmv's cxpcrinlental data(61 proves to be considerably better than that obt,ained with past npproximntion tech- niques. ( The accuracy of the technique is investigated further by comparing calculations for isotropic elastic discs with some exact equivoluminal modes of such discs. C;\r,cur~cs OF Ii.i~~.\~~~~~ IS ELECTROELASTIC ~TI13R.4TIOXS