Volcanic explosions are accompanied by strong acoustic pressure disturbances in the atmosphere. With a proper source model, these acoustic signals provide invaluable information about volcanic explosion dynamics. Far-field solutions to volcanic infrasound radiation have been derived above a rigid half-space boundary, and a simple inversion method was developed based on the half-space model. Acoustic monopole and dipole sources were estimated simultaneously from infrasound waveforms. Stability of the inversion procedure was assessed in terms of variances of source parameters, and the procedure was reliable with at least three stations around the infrasound source. Application of this method to infrasound observations recorded at Tungurahua volcano in Ecuador successfully produced a reasonable range of source parameters with acceptable variances. Observed strong directivity of infrasound radiation from explosions at Tungurahua are successfully explained by the directivity of a dipole source model. The resultant dipole axis, in turn, shows good agreement with the opening direction of the vent at Tungurahua, which is considered to be the origin of the dipole source. The method is general and can be utilized to study any monopole, dipole or combined sources generated by explosions.