The present work addresses the structural damage identification problem in plates by using the flexibility matrix. The damage is continuously described by a cohesion parameter defined in the elastic structure domain. The damage identification problem is, then, defined as an optimization one, whose aim is to minimize, with respect to the cohesion field, a functional based on the difference between the experimental flexibility matrix and the corresponding one predicted by a finite element model of the structure. The particle swarm optimization method was considered to solve the optimization problem. The numerical tests of the proposed damage identification method are carried out taking into account a rectangular Kirchhoff plate with one clamped edge. The considered damage scenario is composed by two damaged regions and the mode shapes are corrupted with different additive noise levels. The numerical results show the potentiality of the proposed method in identifying damages from a reduced number of noise corrupted experimental data.