To address the dynamical instability of single-layer latticed shells under earthquake excitation, proceeding from the damage accumulative effect of steel material, the constructive relationship between strain and damage was first set up on the basis of the theory of both plastic strain and energy dissipation. Then, the criterion for dynamic stability by means of B-R kinetic criterion in combination with plastic strain energy density was put forward. The method of incremental dynamic analysis was used to study the dynamic stability of a Kiewitt-8 type single-layer latticed shell under earthquake excitation when considering the damage accumulation effect. Finally, some conclusions are obtained that strain-damage constitutive mode can reflect the features of structural failure and greatly affect the structure, which may be helpful in engineering repair and the estimation of seismic capacity.