ROCK CAVE, W.Va. (AP) _ Conservation officers brought two bear carcasses to the West Virginia Wildlife Center last week. Added to the 13 bears already executed since late- April, the bodies are grim testimony to a bear repopulation program that has worked too well.

Fifty years ago, black bears were scarce in West Virginia. Now, the Mountain State is crawling with bruin who are killing sheep, destroying bee hives and devouring doughnut handouts.

The Department of Natural Resources has succeeded in getting West Virginians to view bears for something other than target practice. But conservation officials acknowledge the state has failed to teach West Virginians to live with bears.

''The things we did worked just tremendously well. We never thought it would work this well in our wildest hopes,'' said DNR biologist Joe Rieffenberger. ''Now we may have oversold people on bears.''

Conservation officers who worked so hard to get West Virginians to stop killing bears now must lead hunting parties to track bears down.

The bears are being killed for behaving like bears.

''Primarily it's because of the general public's ignorance about bear biology and bear habits. Man either intentionally or unintentionally creates an attractive food source,'' said Bill Vanscoy, who runs the DNR's state wildlife center, formerly known as the French Creek Game Farm.

Vanscoy receives daily reminders of West Virginia's new bear problem in the form of orphaned bear cubs and the carcasses of executed trouble bears.

''Bears are interested primarily in groceries and other bears. If there is food to be had a bear is a big strong animal and will do what it can to to get the food,'' he said.

Rieffenberger has received reports of 11 bears that have been killed by the DNR since April 22. He is awaiting the paperwork on another four.

''It's going to be a bad year,'' he said. ''This is only a month of it.''

In all of 1987, just 15 bears had to be killed.

Rieffenberger is worried about backlash from a fickle public, which loves a bear only so long as it doesn't overturn a garbage can or rip open a screen door.

''When they hear we've killed 15 bears or more, then they start getting on their high horse. They want to protect the neighborhood bear, so to speak. People are very bad about feeding a bear,'' he said.

Rieffenberger said he is afraid West Virginians will return to the philosophy that a bear is a varmint and the only good varmint is a dead varmint.

''The backlash is something I always fear,'' he said. ''That attitude is a pioneer aspect of West Virginia, and it's not buried too deep in people.''

The troubles increase as the bear population continues to grow.

Rieffenberger advocates a change in the hunting season so that more bears will be killed - ''to keep it from being a runaway growth, because our bear population still is growing.''

But what he really wants is another change in West Virginians.

''I'd like to see Red Ryder give everybody a BB gun and give the bear a good sting. Teach them to fear people and stay away.'

DNR officers this week hunted down a sheep-killing bear in Randolph County and in the process flushed another bear ''who got in the wrong place at the wrong time.'' Both were killed.

''This poor innocent fellow was one we had tagged last July,'' Rieffenberger said. ''He weighed 242 pounds then and we weighed him now at 295. At least we got some information out of him in death.''

The sheep-killing bear weighed just 110 pounds - unusually small to be going after mutton, Rieffenberger said.

''There's been eight bears killed so far this year for getting into sheep. The lightest one weighed 180 pounds. And they all were males,'' he said.

''It's not unusual for bear to kill sheep. Unfortunately, it's a bit too common.''

The DNR is perplexed. The sheep killers are large, well-fed older bears. No one knows what prompts bears to start hunting sheep, but once they start, it's certain they will continue.

The DNR has tried trapping trouble bears and relocating them, but West Virginia is too populated. ''Really, there's no place to move them to. We just gave that up,'' Rieffenberger said. ''Now we just eliminate the problem.''

DNR officers are unhappy about that, especially when they have to kill a bear simply because people have taught it to be friendly.

A neighborhood outside of Charleston last year fattened a gregarious bear with doughnuts, popcorn and even fresh-baked pies. The DNR had to hunt it down and kill it when it started hanging around and startled a woman.

Another bear in the same county was executed this year for similar reasons.

''I hate it when it's like that. Yes, they are killed by kindness,'' Rieffenberger said.

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