The pressure pulse produced by a large explosion in the atmosphere is investigated. The explosion is represented in terms of the excess pressure and normal velocity on a closed surface, outside of which the hydrodynamical equations are linearized. The pulse is represented in terms of a Fourier transform of the associated harmonic frequency problem, for which a ring-source Green's function is obtained in terms of an expansion of the discrete modes. It is shown that the excess pressure may be represented in terms of an integral (containing the Green's function) over the surface surrounding the source. The gravity wave portion of the pressure pulse at the ground is computed for various ranges from the source, which is located at various altitudes, and for three models of the atmosphere. In calculating the head of the pulse a new asymptotic technique is introduced which gives very good results for intermediate and long ranges.