The oil drilling industry, which took a dramatic dive in the recession, is showing faint signs of recovery--an improvement based in part on the belief that oil prices may have stabilized.

But after a precipitous decline that left oil field equipment manufacturers, steel pipe makers, independent producers and banks staggering, industry officials and analysts are extraordinarily cautious about predicting a turnaround.

"There are an awful lot of people who got themselves overextended, and when you're in that position you tend to wait for the positives to materialize rather than speculate about them," said Lloyd Unsell, executive vice president of the Independent Petroleum Association of America.

"I think it has turned," said Thomas A. Escott, a Paine Webber Mitchell Hutchins industry analyst in Dallas. But he added, "People are reluctant to forecast a strong recovery because the forecasting has been so bad . . . It doesn't feel very good to feel like a fool, to watch this thing melt away as if it had no bottom."

The key sign of a recovery so far is the Hughes Tool Co. oil rig count, a barometer of industry health. From a high of 4,530 in the final week of 1981, the rig count dropped steadily, reaching 1,807 in the week ending last April 18. The industry hopes that marks the bottom.

Since then, the count has moved up in a saw-tooth pattern to 1,959 last week.

"I think the rig count has flattened. It's no longer dropping," said Ike Kerridge, an economist who is vice president for stockholder relations for Hughes. But he added that, at the current level of drilling, the industry is replacing only about 65 percent of production, "inviting problems down the line."

Like others in the business, Kerridge pointed to two major factors that will determine the outlook--the stability of the price of oil, now about $28 to $29 a barrel, and the demand for natural gas, which has been reduced by the recession--increasing competition from oil as oil prices have fallen--and a mild winter.

"People just are not going to drill gas wells if there is no market for it," Kerridge said.

Another factor that may help increase the number of oil and gas wells being drilled is the reduction in the price of drilling that accompanied the disaster in the oil patch.

"Exploration and production will come back. We're not looking for a boom in drilling anytime soon, but we are expecting the industry to regain its health gradually," said Carol T. F. Bennett, an economist with Houston's Texas Commerce Bank."It's starting to creep upward as there is less concern about oil prices actually falling."

The decline in the price of oil from about a year ago when it was approximately $34 has been partially offset by the decline in the cost of drilling. "It's approximately as possible to produce oil now as it was during the boom," she Bennett said.

In 1981, the average cost per foot for well completion was $94.30, reflecting the inflation in equipment prices when drilling was fast and furious. The cost for 1982 has been estimated at $76 to $78 by Hughes and is expected to drop to about $70 this year.

Compared with the era when drilling costs "were going through the ceiling, they have tended to come down," said Unsell of the IPAA. "Those who do have the cash flow positions that are comfortable are able to drill at a somewhat lower cost," he said.

Those who don't have cash are facing increased difficulties in raising money from investors, whose enthusiasm for drilling ventures probably has been cooled by more restrictive tax shelter provisions. Moreover, bankers who were scared by the failure of Penn Square National Bank in Oklahoma and loan problems at other banks who rushed into the energy area during the boom are likely to move more slowly this time.

"We've always taken a conservative approach to lending to energy companies and others," Bennett said. That strategy served Texas Commerce well in "boom and not-so-boom," she said. Other banks found themselves in a less comfortable position.

"We're still living under the curse of the $100-a-barrel oil price myth," said Bill Sallans, executive vice president of the Petroleum Equipment Suppliers Association. "That drew all sorts of crazy money in. But try to get a bank to put some in now if the bank doesn't know the business."

The last to recover from the oil drilling bust will be the equipment manufacturers, who are still holding large inventories that are difficult to unload even at lower prices.

In Texas, employment in oil field equipment manufacturing peaked at 89,700 in March, 1982. In March, 1983, it was 49,000. "We've got uncertainties that are just keeping people from making decisions," said Sallans, who doesn't see immediate recovery written in the rig count. "I'd love to just do a job here and claim great things, but there's just no reason to."