In this paper, the Lothe–Barnett’s integral formalism is extended to solve the surface wave problem of a prestressed piezoelectric material. By using the electroacoustoelasticity, the effective material constants and the mass density in the prestressed initial state are determined, and then the surface wave velocities of a prestressed piezoelectric crystal can be obtained by the integral formalism. Under some limitations, the properties of the integral matrices derived in the Lothe–Barnett’s integral formalism are shown to be valid for the prestressed piezoelectric crystal. A computer program is implemented to calculate the surface wave velocities of a prestressed X‐cut lithium niobate (LiNbO3) crystal. Finally, a possible application of the electroacoustoelastic effect to the design of a delay‐controllable delay line is proposed.