Because of the zone of damage that is created around an explosion it is unlikely that simple elastic reflection of seismic waves takes place at the free surface, at least for small angles of incidence. Some attempts have been made to simulate the effect on P‐wave radiation of the zone of damage but so far the only models used have been acoustic. Here we construct a fully elastic model. The damaged zone is represented in a highly simplified way by a horizontal screen centred on the source, which attenuates signals reflected back from the free surface. P‐waveforms are computed for various angles of emergence using the Kirchhoff approximation. Two types of screen are considered: for one—the opaque screen—the downward radiation is reduced to zero over a circular area of radius a, and for the other the radiation at the level of the source is reduced by a factor [1 – exp(–r2/a2)], where r is the distance of a point on the screen from the focus and a is a constant, the scale size of the screen. This model is referred to as the semi‐opaque screen. For steep take‐off angles the arrivals generated by diffraction by the screen of pP and pS to P, are of significant amplitude relative to P and have negative polarity. For the opaque screen the principal contributions to these arrivals arise from diffraction at the near and far edges of the screen, of rays travelling in the vertical plane containing the focus. As the angle of incidence from source to receiver increases, the contributions from the far edge of the screen become insignificant. In the lit zone the diffraction of pP at the near edge produces arrivals with significant amplitudes and positive polarity for angles near the shadow edge. The change from negative to positive polarity in moving from the shadow zone into the lit is predicted by generalized ray theory. The results for the semi‐opaque models are smoothed versions of those obtained for the opaque model. In addition to the impulsive arrivals the computed responses show a positive low‐frequency step with an onset around the time of the first diffracted arrival generated by pP. Examples of seismograms computed for the opaque screen model using explosion source functions show some features of observed seismograms. Copyright © 1990, Wiley Blackwell. All rights reserved