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• An omnidirectional high-order SH wave piezoelectric transducer (OSH n -PT) was proposed. • The excitation function of the OSH n -PT was derived explicitly. • Simulations and experiments validate the significant mode selectivity of the OSH n -PT. • The SNR of the OSH 1 -PT was over 19 dB in pitch-catch tests (30.7 dB at 490 kHz). • An OSH 2 -PT was theoretically designed and validated by FE simulations. Guided wave tomography, as an advanced structural health monitoring (SHM) method, has offered a feasible solution to wall thickness quantification which is essential in petrochemical industries. However, previously used low-frequency Lamb waves (A 0 and S 0) limit the resolution of tomography. Recently, the first-order shear horizontal guided wave (SH 1) was found very promising in tomography for its capability in resolution improvement. However, the SHM-required omnidirectional piezoelectric transducers for selectively generating and receiving the SH 1 wave, namely OSH 1 -PT, are not available yet. In this work, a general method was developed to design an OSH 1 -PT based on the thickness-poled PZT half-ring configuration. Firstly, the excitation function of the OSH 1 -PT was explicitly derived and validated through finite element simulations. Secondly, a design formula was obtained and used to determine the size of the OSH 1 -PT. Then, the designed OSH 1 -PT was fabricated and tested by using a 2D laser Doppler vibrometer. Significant mode selectivity was observed in all directions (0 ∼ 90°) with the excited SH 1 to SH 0 ratio higher than 15 dB. Pitch-catch tests were conducted from 400 ∼ 520 kHz and the received SH 1 to SH 0 ratio was found higher than 19 dB at all frequencies and reached its maxima of 30.7 dB at 490 kHz, which is very close to the designed working frequency of 500 kHz. Finally, an OSH 2 -PT was theoretically designed and validated by FE simulations. Due to its simplicity and effectiveness in designing the OSH n -PT, the proposed method is expected to pave the road to wide applications of high-order SH wave tomography. [ABSTRACT FROM AUTHOR]