To address the problem that existing airport runway bearing capacity evaluation relies on periodic inspection and is difficult to continuously reflect changes in pavement structural condition, a dynamic bearing capacity evaluation method for runways based on real-time mechanical perception was proposed. First, the layout scheme of runway monitoring sections and sensors was optimized according to aircraft motion characteristics and taxiing trajectories. On this basis, finite element simulation was adopted to analyze the relationships among base-top perceived stress, displacement responses of pavement structural layers, and pavement structural parameters during the taxiing of two commonly used aircraft types, namely B737-800 and A320. Subsequently, full-scale test data from Construction Cycle 1 (CC1) of the National Airport Pavement Test Facility (NAPTF) in the United States were used as a benchmark to comparatively validate the load inversion model. Finally, based on the load inversion model and displacement perception model, an integrated analysis method of “load identification–subgrade modulus inversion–bearing capacity evaluation” was established. The results show that arranging monitoring sections within 100–150 m from the runway end can realize complete monitoring of the takeoff and landing stages. Aircraft load and surface slab thickness are the main factors affecting the base-top perceived stress. The CC1 full-scale test results under three subgrade strength conditions were used to verify the reliability of the load inversion model, and the errors between the inverted wheel loads and the actual wheel load were approximately 3%. Surface slab thickness and subgrade modulus have significant effects on the peak dynamic displacement of the pavement. When the surface slab thickness increases by 25%, the dynamic displacements of the surface layer, base layer, and subgrade decrease by approximately 15%; when the subgrade modulus increases by 80 MPa, the reduction in dynamic displacement exceeds 50%. Combined with the load inversion model, the subgrade modulus can be inverted from the dynamic displacement perceived by sensors. Furthermore, a runway bearing capacity evaluation method based on the dynamic mechanical perception model was established and verified using long-term monitoring data from an airport, with an error of less than 5%. The results indicate that the proposed method can connect field mechanical perception data with pavement bearing capacity evaluation parameters, provide a technical basis for real-time perception and dynamic updating of runway bearing capacity, and offer technical support for runway structural condition monitoring, bearing capacity variation analysis, and maintenance decision-making.