The site had struggled through the evening and became increasingly slow, and was taken offline altogether at 10pm.
"We are currently working to improve the Dream Team website," said a statement from The Sun.
"To help speed up this process, we have temporarily taken the site offline. We are sorry for any inconvenience. Please check back later."
Haran Sold, managing director for EMEA at internet performance company Keynote Systems, said: "Similar problems occurred on The Sun's Dream Team website during the final registrations for the start of 2005/2006 Premiership fantasy league.
"Almost identical events as last night meant the website crashed under the heavy load, and some registrations were not possible."
Keynote Systems said that load-testing sites before these kinds of events is imperative because any deadline means there is always a very large influx of users logging on at one time.
"For a fantasy football league, where fans will wait as long as possible before entering to ensure that the team they pick is the best possible, and that all players are fighting fit, it is crucial that sites are built to cope," said Sold.
"With many other websites offering leagues for the World Cup, it is possible that frustrated fans may have decided to move to another site during the Sun's three hours of downtime."
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