Damage detection at the early stages of structural design is crucial to prevent the occurrence of unpredictable failures. The residual error method can be used to detect damage by monitoring the changes it induces in the equation of motion. The residual error method was originally applied to beam structures, but in this study, it is adapted to detect and locate damage in two-dimensional structures such as plates. To demonstrate this method, the damage is modeled as a reduction in stiffness while the mass is maintained at a constant value. The effect of damage on the equation of motion of the intact structure is then quantified by substituting the eigenmodes and eigenvalues of the damaged structure; the residual error then pinpoints the location of the damage and its relative severity. Thorough finite element method simulations are performed to assess the robustness and limitations of the method in several scenarios with single and multiple damages. Furthermore, the sensitivity of the method to various noise levels is tested. Finally, a comparison is drawn between the residual error method and the absolute difference mode shape curvature method. The obtained results show that the residual error method is able to detect and locate damage in one- and two-dimensional structures.