Here are comments that you should find useful for other authors:

To use bibtex: Here it's a disaster.  
In any case I succeeded and here's how I did it:

In the tex file insert:
\usepackage{natbib}
Also as usual, in the tex file you must have
\bibliography{YOUR_BIB_FILE_NAME}
I've attached the bst file (also available from the Elsevier site)
elsart-num.bst
So far so good. BUT then both .cls files fail to insert the proper command
in the .aux file for bibtex to operate. So after you've latexed the file,
go to the .aux file and add one additional line to the file with the
following text:
\bibstyle{elsart-num}
This must be done every time you run bibtex, since the aux file gets
rewritten with every latexing. I imagine there's some way to modify the
.cls file to do this properly (after all revtex does it), but I'm not
enough of a hacker to figure that one out.