Modern civil, transport, and aerospace engineering structures are becoming more complex and multifunctional and are expected to be fully functional under severe environmental conditions. Their failure can lead to tragic consequences and therefore structures have to undergo regular inspections. Rigorous inspection of structures on a regular basis is usually a time-consuming and costly procedure; therefore non-destructive structural health monitoring (SHM) methods have become an important research area in civil, mechanical and aerospace engineering communities. In recent years, various vibration-based damage detection methods have been proposed for SHM. These methods are based on the fact that dynamic characteristics, i.e., natural frequencies, mode shapes and modal damping, are directly related to the stiffness of the structure. Therefore, a change in natural frequencies or a change in mode shapes will indicate a loss of stiffness. In this paper, a mode shape curvature based method for detection and localization of damage in beam-like and plate-like structures is described. The proposed algorithm requires only the mode shape curvature data of the damaged structure. The damage index is defined as the absolute difference between the measured curvature of the damaged structure and the smoothed polynomial representing the curvature of the healthy structure. To examine the advantages and limitations of the proposed method, several sets of numerical simulations are carried out. Simulated test cases considering different levels of damage severity, measurement noise and sensor sparsity are studied to evaluate the robustness of the method under the noisy experimental data and limited sensor data. The modal frequencies and the corresponding mode shapes are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer (SLV) for the experimental study.