This article deals with the study of vibration, buckling, and dynamic instability characteristics in damaged cross-ply and angle-ply curved laminates under uniform, uniaxial follower loading, using finite element approach. First-order shear deformation theory is used to model the doubly curved panels and is formulated according to Sandars' first approximation. Damage is modelled using an anisotropic damage formulation. Analysis is carried out on plate and three types of curved panels to obtain vibration, buckling, and dynamic instability (flutter) behaviour. The effect of damage on natural frequency, critical buckling load, flutter load, and flutter frequency is studied. The results show that the introduction of damage influences the flutter characteristics of panels more profoundly than the free-vibration or buckling characteristics. The results also indicate that, compared to undamaged panels, heavily damaged panels show steeper deviations in stability characteristics than mildly damaged ones.