This user guide explains how to use the CHIEF2004 computer program. CHIEF2004 is an update of the CHIEF2000 program Benthien, Barach, and Hobbs, 2000. The program was tested on machines running Windows 95/98 , Windows NT, and COMPACT UNIX. The CHIEF program was originally developed in the 1960s to compute the acoustic radiation from an arbitrary shaped radiating body. The program was extensively updated in 1988 and a users manual was published Benthien, Barach, and Gillette, 1988. This CHIEF manual is still an excellent reference for those interested in the details of the CHIEF program and the underlying theory. The original CHIEF manual was included in the CD-ROM document Benthien and Barach, 1998. The CHIEF2000 manual was published as an Adobe Acrobat document Benthien,Barach, and Hobbs, 2000. The original CHIEF program and the 1988 update were essentially a library of Fortran subroutines that were called from a user-generated control routine. This approach gave the user a lot of flexibility, but required a Fortran compiler to compile and link the control routine with the library routines. The presence of a Fortran compiler was not a big problem on most main frame computers. However, with the increasing use of PCs and workstations for numerical computation, the presence of a Fortran compiler can no longer be assumed. Thus, both CHIEF 2000 and CHIEF2004 are compiled executable programs that rely on a user-generated ASCII text file for input. While this approach gives up some flexibility, we have included as many features of the previous versions of CHIEF as possible.