Structural damage detection is of great significance for engineering applications. Most damage detection methods are vibration-based methods. In this paper, we propose a method for damage detection of structures under static loads. The wavelet transform technique is introduced in the spatially distributed strain energy signal processing. We can use the singularity of wavelet coefficients to determine the damaged location. Numerical examples under four cases of damages are provided to illustrate the applicability of the proposed method. We use the element stiffness reduction to simulate the damage. The results of the damaged cases have indicated that the different damage locations in a structure can be precisely determined using the proposed method. The damage detection method proposed in this paper can be introduced for engineering applications.