Based on the peridynamics theory, the progressive damage process of theradome laminated composite structure under the impact of high-speed small flying objects isanalyzed, The influence of the flying object shapes to the material damage mode and theflying object residual velocity is considered. The simulation results show that the radomeaminated composite materia structure will be penetrated under the impact of high-speeosmall flying objects. The main damage mode of the composite structure is matrix damageThe form and degree of damage expansion change gradually with the penetration time. Theflying object shapes have significantly impact on the damage form and degree of the material.