Billy Mayfair, who led after the first round, carded seven points in the second round. He shares second place at 22 points with Brandt Jobe (nine points) and Charles Howell III (10). Chris Anderson, David Toms and Heath Slocum share fifth place with 18 points
After Thursday's play was completely washed out, the first and second rounds were pushed back one day with the final 36 holes scheduled for Sunday.
The cut fell at 60 players and ties, instead of 70 and ties. The second cut, which would have happened after round three, is not going to happen this year due to the weather problems on Thursday.
The International uses the modified Stableford scoring system in which players are awarded eight points for double-eagles, five for eagles and two for birdies. They lose one point for bogeys and three points for double-bogeys or worse.
Beckman began his second round on the back nine at Castle Pines Golf Club. He tripped to bogeys on 12 and 13, after missing both greens, to drop back to eight points, but got those two points back with a birdie on the par-4 15th.
The 2001 Southern Farm Bureau Classic winner two-putted for birdie from the fringe on 17 to move to 12 points. Beckman then sank a 15-foot eagle putt on the par-five first to leap to 17 points. He birdied the second and fourth to move to 21 points.
Beckman parred his next two holes, then birdied the par-three seventh from 20 feet out to get to 23 points before he parred his final two holes.
'I've just been into trying to make points,' Beckman said. 'This format is interesting in that I couldn't tell you what I shot either day, and so when you get in that frame of mind, you play well. I've played No. 1 well, and fortunately I eagled the (par-four) sixth Friday, which was a bonus.'
Mayfair, who celebrated his 39th birthday Saturday, also started on the back nine and birdied the 10th. He came back with a birdie on the par-four 13th to move to 19 points.
The five-time winner on the PGA Tour dropped a point at the 15th with a bogey, but came right back to birdie 16 and 17. Mayfair tripped to another bogey on 18 to fall back to 21 points.
Around the turn, he birdied the first before bogeys on three and four. Mayfair moved to 23 points with a birdie on the seventh, but he three-putted for bogey on the ninth, his last, to share second.
'I did putt well,' Mayfair said. 'I didn't hit it quite as well today. I didn't drive it as well. The par-threes is when I hit it close and made birdies.'
Jobe started on 10 and bogeyed three of his first four holes to slide back to 10 points. He got two points back with a birdie on the 14th before the UCLA alum moved to 14 points with a birdie on the par-five 17th.
The 39-year-old ran off three birdies in a four-hole stretch from the third to jump to 20 points. Jobe, who owns nine international victories, birdied the ninth to share second place.
'I misclubbed every single hole for the first four or five holes, and then I was like, all right, let's figure this out here,' said Jobe. 'That's kind of what I did. I was giving up too much yardage-wise, just a bad start. I did the same thing Friday.'
Like the other three near the top of the leaderboard, Howell started on 10. He dropped in birdies on 10 and 11 to move to 16 points. He drained another birdie try on 14, but slipped to a bogey at 16 to make the turn with 17 points.
The 26-year-old ran in back-to-back birdies from the third. Howell carded his final birdie on the seventh to get to 23 points, but faltered to a bogey at the next, though, to fall one point behind Beckman.
'Today was an important day because largely because Sunday is going to be 36 holes,' Howell said. 'This golf course is tough enough to play when you've got 18 in front of you, but 36 is obviously a very long day.'
Two-time U.S. Open Champion Retief Goosen posted 10 points to move into a tie for eighth place with 17 points and was joined there by U.S. Ryder Cupper Stewart Cink and former Masters champion Phil Mickelson.
The cut was made at seven points, or the top-63 players. Among those missing out on the final two rounds were - Robert Allenby, Justin Leonard and Masters runner-up Chris DiMarco.