Abstract: Rapid and accurate prediction of blast loads on urban buildings is of great importance for post-disaster assessment following accidental urban explosions, including terrorist attacks and industrial explosion accidents, and for improving the comprehensive disaster-prevention and mitigation capability of cities. To enable rapid calculation of blast loads on the blast-facing surface of rigid buildings subjected to far-field explosions, an analytical calculation method was developed based on Hudson’s theoretical blast loading model incorporating rarefaction wave propagation. The original Hudson method was improved for moderate-intensity shock waves by revising the calculations of the incident wave wavelength and rarefaction wave propagation velocity. An incident pressure approximation was further introduced for long duration shock waves to correct the overestimated clearing effect once the calculated surface pressure fell below the incident pressure. In addition, symbolic regression, a supervised machine learning method, was employed to approximate the clearing pressure relation obtained from the Dewitt integral equation. An explicit expression for calculating the pressure-time history on the blast-facing surface was consequently established, avoiding repeated numerical evaluation of the original integral equation and improving the convenience of engineering calculations. The accuracy of the proposed method was evaluated through comparisons with numerical simulations and existing calculation methods. The method was then applied to investigate the spatial distribution of positive impulse over the blast-facing surface and to examine the effects of incident-wave characteristics and building dimensions on the impulse distribution. The results show that, for incident peak overpressures of approximately 100-500 kPa and positive-phase durations of approximately 0.5-2.0 s, the proposed method provides more accurate predictions of blast-facing surface pressure-time histories and impulses than the current standard method and the original Hudson method under most of the investigated conditions. Near the boundary of the investigated applicability range, corresponding to a peak overpressure of approximately 100 kPa, a positive phase duration of approximately 0.5 s, and a relatively large building, the prediction error of the proposed method can be greater than that of the original Hudson method; nevertheless, its deviation from the numerical simulation remains within 20 %. The method therefore provides a reliable calculation tool for rapid damage assessment and blast-resistant design of buildings subjected to far-field explosions.