The safety of airport runways is important to guarantee aircraft taking-off, landing, and taxiing, and the comparison of the mechanical response of pavement structures under dynamic and static loading by LS-DYNA has rarely been studied. The purpose of this work is to separate two analysis methods to investigate the mechanical response of rigid airport pavements. Firstly, a tire–road coupling model of an airfield was established to evaluate the suitability of dynamic and static analyses. Then, the effects of landing pitch angles, sinking speeds, and tire pressures on the effective stress, effective strain, and z-displacement of the runway were investigated for both dynamic and static analysis. Finally, the significance of influence factors was analyzed by regression analysis in Statistical Product and Service Solutions (SPSS). The results indicated that the effective stress, effective strain, and z-displacement of the runway increased with a decrease in the landing pitch angle, which also increased with an increase in the sinking speed and tire pressure. It was demonstrated that the difference in pavement mechanical response between dynamic and static analyses progressively widened at high tire pressure and sinking speed. In other words, the static analysis method can be adopted to assess the dynamic mechanical behavior when the landing pitch angle is large and the tire pressure is small. Among the various factors of mechanical response, the effect of tire pressure was the most obvious, followed by sinking speed and landing pitch angle. The work proposes a new approach to understanding the mechanical behavior of runways under complicated and varied conditions, evaluates the applicability of the dynamic and static mechanical analysis methods, identifies key factors in the dynamic and static mechanical analysis of rigid runways, and provides technical support for improving and maintaining the impact resistance of pavement facilities.