In this work, by making numerical simulations of the Rayleigh-Sommerfeld diffraction integral, we show the finite aperture realization of the recently discovered diffraction-attenuation resistant beams in absorbing media. © 2007 IEEE. 761764M. Zamboni-Rached, Diffraction-Attenuation Resistant Beams in Absorbing Media, Optics Express, 14, pp. 1804-1809 (2006). (Also available as e-print arXiv:physics/0506067 v2 15 Jun 2005)Recami, E., Zamboni-Rached, M., Nóbrega, K.Z., Dartora, C.A., Hernández-Figueroa, H.E., On the localized superluminal solutions to the Maxwell equations (2003) IEEE Journal of Selected Topics in Quantum Electronics, 9, pp. 59-73. , and refs. therein. For a review, seeZamboni-Rached, M., Recami, E., Hernández- Figueroa, H.E., New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies (2002) European Physical Journal D, 21, pp. 217-228. , See, e.gSushilov, N.V., Tavakkoli, J., Cobbold, R.S.C., Propagation of limited-liffraction X-waves in dissipative media (2002) IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 49, pp. 675-682