Abstract A topological insulator with piezoelectric properties is considered, and an action is proposed to find the equations of motion and the constitutive relations of the generalized coordinates of electrodynamic and elastic origin, paying special attention to the restructuring induced by the topological properties. The results are used to demonstrate that the electromechanical factor of the Bleustein-Gulyaev waves on the surface of a topological piezoelectric crystal of class <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>6</mml:mn> <mml:mi>v</mml:mi> </mml:mrow> </mml:msub> </mml:math> in contact with vacuum undergoes a second-order correction in the fine structure constant, associated with the topological properties.