This paper is devoted to the analysis of the dynamics and vibrations of wing-like structures with bonded piezoelectric strips and subjected to unsteady aerodynamic loads for crack detection. Pairs of piezoelectric strips, acting as strain sensors, are bonded at the same locations on the opposite sides of a thin structure executing flexural oscillations. In this crack detection strategy, the measured voltage outputs of the two piezoelectric sensors forming a pair are conveniently subtracted in order to eliminate the voltage corresponding to the same level of strain on both sides. This differential voltage output is used to indicate the presence of a crack in the structure. The nonlinear mechanical behavior of the crack in the compression and extension phases of the oscillatory cycle increases substantially the sensitivity of this detection procedure. Furthermore, this crack detection method can take advantage of the aeroelastic oscillations of the wing structures, which are always present during normal flight evolutions of an aircraft. The numerical analysis of the dynamics of structure subjected to unsteady aerodynamic loads uses a finite element formulation for the structure and the piezoelectric strips and a panel method is used to compute the unsteady aerodynamic loads acting on the oscillating wing structure. Numerical simulation results are presented in the paper to explore the feasibility of this crack detection strategy by using the aeroelastic oscillations of the wing-like structures with bonded piezoelectric strips.