Based on elasto-plastic large displacement analysis method considering the effects of changing axial force, this paper studied the dynamic response and damage mechanism of long span steel deck arch bridge under strong earthquake. Taking two deck arch bridge models—one is two-hinged and the other fixed—with span length of 200m as examples, the dynamic response and plastic damage under strong earthquake waves of the two bridges are calculated. The effects of different analysis procedure, earthquake wave records and design conditions on earthquake response and damage of the bridge are studied. Results show that steel deck arch bridges have preferable seismic resistant ability and occurred limited damage under strong earthquake motion; it is necessary to consider effect of more modes on earthquake response, because of nonexistent of dominant mode in response; the effect of changing axial force on the elasto-plastic response of the bridge can not be ignored when it exceeds 20-30% of yield axial force. Geometric nonlinear have remarkable effect on the moment response of arch rib. By comparing the response of two-hinged and fixed arch bridge, the two-hinged arch bridge takes smaller earthquake load than the fixed arch bridge, because the structure is more flexible and has longer natural period than the fixed bridge. In addition, fixed arch bridge is prone to damage at arch base cross-section, and it is suggested that local buckling prevent measures be taken to keep its load-carrying capability after yield.