In 1990, Larry Mullen (of U2 fame) wrote a song for the Irish soccer
World Cup team, called "Put 'em under pressure" which incidentally
topped the Irish music charts for a record period.

This song was a mixture of:
- The vocals from a previous Scottish soccer 'anthem'.
- The "ole ole" chant popular on soccer terraces.
- A rock guitar riff from Mullen, which actually comes from an old
traditional Irish song played on Uilleann pipes.

I'd really like to know the name of this tune the guitar riff was
based upon.

Many thanks,
Mike.

The guitar riff in "Put 'Em Under Pressure" uses the melody of
"O'Neill's March," also known as "O'Neill's Cavalry March" and
"Máirseáil Uí Néill".

"Based on a traditional Irish tune called O'Neill's march, also used
in the Irish world cup song for Italia '90 (Put 'em under pressure) by
Larry Mullen and Jack Charlton."

On-Line Guitar Archive
http://www.olga.net/dynamic/browse.php?local=main/h/horslips/dearg_doom.tab

You can verify that this is the correct melody by listening to a midi
of "O'Neill's March", and comparing it to an mp3 of "Put 'Em Under
Pressure":

Tadpole Tunes: O'Neill's March
http://tadpole.aus.as/celtic3/oneills.mid

Put 'Em Under Pressure
http://www.mortalwombat.com/Music/PutEmUnderPressure.mp3

Here you'll find the lyrics of "Put 'Em Under Pressure":

U2 Wanderer
http://www.u2wanderer.org/disco/col58_01.html

The alternate names, "O'Neill's Cavalry March" and "Máirseáil Uí
Néill", were found on this site:

The Phantom Piper
http://members.tripod.com/~Hiestand/phantompiper/TUNES.HTM

To locate this information, I began with searches using various
combinations of ""put em under pressure", "larry mullen", "irish",
"uilleann", "song", and "tune". This was the combination which
produced results:

Google Web Search: "put em under pressure" + "irish tune"
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=%22put+em+under+pressure%22+%22irish+tune

Thanks for asking an interesting question. If anything I've said is
unclear or incomplete, or if any of the links do not function, please
request clarification before rating my answer; I'll be glad to offer
further assistance.

Best wishes,
pinkfreud

A great answer, many thanks! You could have got bonus brownie points
by finding an mp3 or sheet music, but I can't fault this answer.

Many thanks again!
Mike.

There was a link to an mp3 included:

"Put 'Em Under Pressure 
http://www.mortalwombat.com/Music/PutEmUnderPressure.mp3 "

Thanks! But I meant an mp3 of the original song (O'Neill's March). 

No matter, all I needed was the song's name, which helped me find the
sheet music which I wanted (if anyone's interested, it's at
http://home.swipnet.se/~w-11382/tunes/oneillsm.gif)

Many thanks again to you both!!
Mike.

While 'Put em under pressure' is a reworking of O'Neill's March, it is
actually a reworking of a reworking. Horselips, a folk/rock band of
the late '70s used it in a song called 'An Dearg Doom' and it was this
tune that was reworked by Larry Mullen to produce the Italia '90
anthem