Outburst of nuclear explosion produces moving air-overpressure above ground surface. These overpressure fronts move at superseismic speeds near ground zero and cause ground motion. Hence, determination of air-blast induced ground displacement is the first essential step in design of underground protective structures in super-seismic zone. For simplified analysis, air-blast load is modelled as linearly decaying pressure with time and using one-dimensional elastic wave propagation model, free-field vertical displacement response of elastic half-space can be expressed as a closed-form solution. However, such a simplified solution seems to be of very little practical utility in addressing problems in geotechnical environment. Hence, a new closed-form solution is proposed for displacement time-history which accounts for linear-inelasticity, plastic wave propagation velocity, and geometric stress attenuation. A conceptual pseudo-static procedure which computes vertical displacement as a static problem at each time instant based on dynamic properties of geomaterials is utilized to achieve the proposed solution. Predictions of the proposed model are compared with results of one of the atmospheric nuclear tests conducted at Nevada Proving Grounds and a reasonable agreement is obtained.