In this paper it is shown how one can use Bessel beams to obtain a stationary localized wave field with high transverse localization, and whose longitudinal intensity pattern can assume any desired shape within a chosen interval 0 less than or equal to z less than or equal to L of the propagation axis. This intensity envelope remains static, i.e., with velocity v = 0; and because of this we call "Frozen Waves" the new solutions to the wave equations (and, in particular, to the Maxwell equations). These solutions can be used in many different and interesting applications, such as optical tweezers, atom guides, optical or acoustic bistouries, various important medical purposes, etc. (C) 2004 Optical Society of America.121740014006