Simple form solutions are obtained for approximate two‐dimensional equations of motion and dominant conditions for free edges of energy‐trapped thickness vibrations of piezoelectric crystal plates. The resulting algebraic frequency equations are employed to calculate frequencies of fundamental and anharmonic overtones of thickness‐shear vibrations in infinite quartz strips of SC cut with a pair of free edges and in rectangular AT‐cut quartz plates with all four edges free. For circular quartz disks with free edge, frequencies of fundamental and harmonic overtones of thickness shear in AT cut, and frequencies of fundamental and anharmonic overtones of thickness shear in BT cut are computed. Presently predicted results are compared with either previously calculated results or existing experimental data. It is found that comparison is very close for all these cases.