The energy flux contained in the P-wave groups (P + pP + sP) or the S-wave groups (S + pS + sS) radiated by a shallow earthquake is modeled assuming that the energy flux in the direct and depth phases adds incoherently. By defining generalized radiation patterns which incorporate this neutral interference, the wave groups are analyzed as though they were comprised of a single phase. Measurements of the energy flux in the wave groups are corrected in the frequency domain for both the body-wave attenuation and the frequency band of the recording. The corrected measurements are then used to estimate the seismic energy radiated by the earthquake. This analysis is applied to digital recordings of the teleseismic wave groups radiated by the May 2, 1983, Coalinga, California, earthquake and the October 28, 1983, Borah Peak, Idaho, earthquake. For the Coalinga earthquake, an estimate of Es = 1.6 ± 0.4×1021 dyn cm was determined from six P-wave groups, while the SH wave group recorded at station COL returned an estimate of Es = 1.2×1021 dyn cm. For the Borah Peak earthquake, an estimate ofEs = 3.2 ± 0.5×1021 dyn cm was determined from seven P-wave groups. The distribution of the isoseismals for the Borah Peak earthquake indicate that the energy radiated by this event was focussed to the northwest, in the direction of rupture propagation. Correcting the teleseismic estimate for this focussing gives Es = 3.6 ± 0.5×1021 dyn cm. Combining these estimates of the radiated energy with broad-band estimates of the seismic moment yields estimates of the apparent stress of 17 and 7 bars for the Coalinga and the Borah Peak earthquakes, respectively.