This paper concerns the development of a computational model for the damage evolution of engineering materials under dynamic loading. Two models describing the anisotropic damage evolution of a material are presented; the first is based on a power function of the effective equivalent stress and the second on the damage strain energy release rate. The methods for computing the damage accumulated in structural components and their implementation in a finite element programme are presented together with some numerical results. The dynamic response of a damaged structural component and the dynamic behaviour of a damaged material have been studied numerically. This study shows that the frequency spectrum of a damaged structure is down-shifted, while the damping ratio of damaged materials becomes higher, the amplitude of the response significantly increases and the resonance ensuing from the damage growth still occurs in a damaged structure.