A method of non-destruction inspection of mechanical structures with vibratory waves for the purpose of detecting local defects and/or changes of state, the method being characterized in that it comprises: - a first training stage, comprising: - defining an inspection zone of a mechanical structure for inspection; - infecting a transient vibratory excitation (Ex) into the inspection zone; - picking up, at different locations of the mechanical structure, the received signals (Se) that are received as a result of infecting the transient vibratory excitation; and - time reversing the received signals (Se) and storing the time-reversed, signals in order to constitute reference excitation signals; - a second training stage, comprising: - simultaneously emitting the reference excitation signals in order to focus them in the inspection zone; and - picking up, at different locations of the mechanical structure, the diverging signals obtained after focusing the reference excitation signals, and storing said diverging signals in order to constitute reference response signals; and - a stage of inspecting the mechanical structure, comprising: · emitting the reference excitation signals in order to focus them in the inspection zone of the mechanical structure; · picking up the diverging signals obtained after the reference excitation signals have been focused; and · comparing the diverging signals with the reference response signals in order to detect the presence or absence of local defects and/or changes of state in the inspection zone of the mechanical structure. - a first training stage, comprising: - defining an inspection zone of a mechanical structure for inspection; - infecting a transient vibratory excitation (Ex) into the inspection zone; - picking up, at different locations of the mechanical structure, the received signals (Se) that are received as a result of infecting the transient vibratory excitation; and - time reversing the received signals (Se) and storing the time-reversed, signals in order to constitute reference excitation signals; - defining an inspection zone of a mechanical structure for inspection; - infecting a transient vibratory excitation (Ex) into the inspection zone; - picking up, at different locations of the mechanical structure, the received signals (Se) that are received as a result of infecting the transient vibratory excitation; and - time reversing the received signals (Se) and storing the time-reversed, signals in order to constitute reference excitation signals; - a second training stage, comprising: - simultaneously emitting the reference excitation signals in order to focus them in the inspection zone; and - picking up, at different locations of the mechanical structure, the diverging signals obtained after focusing the reference excitation signals, and storing said diverging signals in order to constitute reference response signals; and - simultaneously emitting the reference excitation signals in order to focus them in the inspection zone; and - picking up, at different locations of the mechanical structure, the diverging signals obtained after focusing the reference excitation signals, and storing said diverging signals in order to constitute reference response signals; and - a stage of inspecting the mechanical structure, comprising: · emitting the reference excitation signals in order to focus them in the inspection zone of the mechanical structure; · picking up the diverging signals obtained after the reference excitation signals have been focused; and · comparing the diverging signals with the reference response signals in order to detect the presence or absence of local defects and/or changes of state in the inspection zone of the mechanical structure. · emitting the reference excitation signals in order to focus them in the inspection zone of the mechanical structure; · picking up the diverging signals obtained after the reference excitation signals have been focused; and · comparing the diverging signals with the reference response signals in order to detect the presence or absence of local defects and/or changes of state in the inspection zone of the mechanical structure.