A lack of sponsorship is forcing the team to suspend operations Monday morning on the No. 28 Ford, team general manager Max Jones said before Sunday's race. Kvapil finished 18th and his team is 39th in the owner standings.
"It's not exactly a surprise," Jones said. "We said all along we'd do five races and try to find something, and we just haven't found anything yet to run another five. We've got some things in the works, but nothing has come together fast enough."
Jones did not rule out reviving the race team if funding eventually comes through.
"If we get something, we'll bring it back," he said. "But we just don't have anything right now."
Kvapil has been without proper funding for more than a year. Yates and partner Roush Fenway Racing had to piece sponsorship together on a race-by-race basis, and the team finished a commendable 23rd in the standings without ever having full funding.
But the decent season wasn't enough to attract sponsors, and the team was overhauled during the offseason when Paul Menard signed on to expand the team to three cars and then Bobby Labonte came aboard in a partnership between Yates and Hall of Fame Racing.
Labonte received the points Kvapil earned last year, and Kvapil was forced to qualify on speed for the first five events of this season. He missed the field at Las Vegas, then blew a motor at Atlanta to fall into a deep hole in the points.
It's not immediately decided what will happen to the crew members who work on Kvapil's team. Many could simply be shuffled into new roles with Yates or Roush.
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MORE ENGINE WOES: Greg Biffle, already nursing bruised ribs all weekend, couldn't do the same with his motor.
Biffle's car suffered its second engine failure this season and exited Sunday's race after 326 of the 500 laps. He finished 39th.
"I would have never thought you'd have engine trouble at Bristol. It never crossed my mind," he said. "We were running along and I think we were 11th, but we had a top 10 sewn up, easy. I was kind of riding around waiting to get to the end."
Biffle also had an engine failure at Las Vegas in the third race of the season. The pair of DNF's have dropped him to 18th in the points.
He came to Bristol with bruised ribs sustained when he slipped earlier this week on a dock while jumping into a boat, and the soreness caused him to pull out of the Nationwide Series race on Saturday. He said he felt OK after the Cup race, but wasn't sure there was more pain to come.
"I'm sure if you ask me tomorrow, I'm going to be in a tremendous amout of pain, I promise you," he said. "But there's no problem at all driving the car."
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BACK ON TOP: Robbie Loomis returned to the top of the pit box for the first time since 2005 when he filled in as crew chief for Elliott Sadler.
Loomis stepped in for Kevin Buskirk, who was feeling ill all weekend and left Bristol on Saturday night. Loomis, vice president of Richard Petty Motorsports, last worked as a crew chief for Jeff Gordon in 2005.
"I hope I remember what to do," he joked before the pre-race driver meeting.
His temporary assignment took NASCAR by surprise: Race director David Hoots called for "the crew chief of the (No.) 19" as he took role at the driver meeting, and seemed surprised when Loomis raised his hand.
"I'm not going to say a word," Hoots replied to a scattering of chuckles.
Buskirk returned to North Carolina to be checked out, and Loomis had been involved with Sadler's team all weekend just in case he had to step in. Although he led radio communication with Sadler, pit strategy was done by committee.
Sadler finished 20th.
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OFF THE BUBBLE: Ryan Newman and Mark Martin both used strong runs Sunday to move off the bubble for the all-important top-35 mark.
Martin finished sixth and Newman was seventh, assuring both of them spots in the field for next weekend's race at Martinsville Speedway. Only drivers locked inside the top 35 in owner points are assured a spot in the race: everyone else must qualify on speed.
"I had fun today," said Martin, who moved up four spots in the owner standings to 31st. "It is just great for this team to get some forward momentum. But it was pretty awesome, that car was rolling on those long greens."
Martin has had horrendous luck in his first month with Hendrick Motorsports. Two blown motors and a cut tire derailed the start of his season, putting him in a deep hole in what many had thought would be a championship-contending season. But he won the pole at Bristol, his second straight race in the top starting spot, and parlayed it into a solid finish.
Newman's luck hasn't been much better, and he came to Bristol 32nd in owner points. But his Stewart-Haas Racing team worked hard to give him a solid car this week, and he responded with a second-place qualifying effort and a solid run.
"I'm happy for all the guys on the (No.) 39," team owner Tony Stewart said. "They've all been working hard, and it's hard to not let your morale get beat up having the kind of bad luck they've had. It was good to see them get a good run like they deserved."
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IN TROUBLE: Scott Speed has his work cut out for him next week at Martinsville: The rookie finished 28th on Sunday, is outside the top 35 in owner points and will have to qualify on speed at a very challenging race track.
"I tried not to hit anything," Speed joked of his first Cup race at Bristol.
At just 21 points outside of 34th place, Speed needs one solid run to get his Red Bull Racing car locked into the field.
Also outside the top-35 going into Martinsville, the first race where this season's points count, is Aric Almirola and Paul Menard.
Almirola doesn't have the sponsorship to guarantee a full season, but Menard is racing in a fully funded car for Yates Racing.