We estimated radiated seismic energy (E(s)) from 18 shallow, thrust Mexican subduction zone earthquakes (4 X 10(22) less than or equal to M(0) less than or equal to 1.1 X 10(28) dyne-cm; 11 less than or equal to H less than or equal to 37 km) using digital accelerograms from the Guerrero Accelerograph Array and neglecting stations with large site effects. E(s) is computed by integrating squared velocity spectra, after applying geometrical spreading and Q corrections. We discarded epicentral recordings for the largest Michoacan event. We find that log (E(s)/M(0)) = -4.152 +/- 0.275, which gives a median value of E(s)/M(0) and apparent stress (sigma(a)) of 7.1 x 10(-5) and 24 bars, respectively. The median E(s)/M(0) value is in accordance with Gutenberg and Richter's (G-R) (1956) formula for E(s), in which E(s)/M(0) = 5 x 10(-5) is implicit. Worldwide E(s)/M(0) data, where E(s) is computed from local records, mostly fall between 5 x 10(-5) and 5 x 10(-4) for events with M(0) greater than or equal to 10(22) dyne-cm. On the other hand, E(S)/M(0) values, generally, lie between 5 x 10(-6) and 5 x 10(-5), if E(s) is estimated from teleseismic records. Especially anomalous are the E(s)/M(0) data from Kikuchi and Fukao (1988) for large and great earthquakes, which fall near 5 x 10(-6). Thus, while E(s) from local data suggests that the G-R relation seldom overestimates seismic energy release, the teleseismic data point to the contrary. The cause of this discrepancy may lie in the difficulty of resolving incoherent radiation from the fault and inappropriate choice of t* in the analysis of teleseismic data.