With the rapid development of high-rise buildings, elevator steel belts have been widely adopted due to their advantages of low weight, high strength, small bending radius, and low operating noise. However, during long-term service, internal steel wires are prone to fracture, forming broken wire defects that compromise structural integrity and threaten operational safety. Existing detection methods such as magnetic flux leakage (MFL), ultrasonic guided waves, and eddy currents often rely heavily on external sensors, which suffer from complex deployment and limited sensitivity, making it difficult to reveal the internal damage mechanism through structural response. This study proposes a damage identification method based on two-dimensional wave modeling combined with finite difference simulation. The anisotropic composite nature of the steel belt is first homogenized using the rule of mixtures, and a 2D in-plane wave equation is derived. The control equation is discretized using an explicit central difference scheme, and time-domain responses, frequency spectra, envelope curves, and energy distributions are obtained for both healthy and damaged cases. Simulation results demonstrate that broken wire damage leads to reduced wave speed, decreased response amplitude, frequency downshifts, and energy dispersion, all indicating strong damage sensitivity. The proposed method relies on the intrinsic wave response of the structure itself without requiring external sensors, offering a promising theoretical and technical approach for early damage identification in elevator steel belts.