Based on the ω⁻² and ω⁻³ source models, we explore the effect on estimates of seismic radiation energy, E_s , caused by finite frequency bandwidth limitation of source spectra. Let f_c be the corner frequency of a source spectrum and f_u and f_c are, respectively, the upper and lower bounds of a frequency band in use. Results show that the effect depends on f_u/f_c and f_l/f_c , and E_s is under-estimated when f_l > 0 and f_u < ∞. When f_u/f_c < 20, the effect is sensitive to both f_l/f_c and f_u/f_c for the ω⁻² source model, but mainly to f_l/f_c for the ω⁻³ model. When f_u/f_c > 20, the effect is insensitive only to f_u/f_c for the two models. Let E_s' be the seismic radiation energy estimated without removal of finite frequency bandwidth limitation. Results show: (1) E_s'/Es first slightly increases and then decreases with increasing f_c ; or (2) E_s'/Es monotonously decrease with increasing f_c. For the 1999 M_s 7.6 Chi-Chi earthquake, Taiwan, Es was under-estimated by Hwang et al. (2001), and the degree of under-estimates varies from station to station.