Your greatest concern after fishing Yellowstone Park for three or four days in what to do about the lacerated index finger and thumb of your left hand. After you extract flies from the toothy mouths of several hundred cutthroat throat, their dentures have left a crimson lattice-work of nicks and gashes.

The solution lies close at hand. Abandon the easy spectacular fishing for cutthroat and drive to one of the legendary brown trout streams in the Park, such as the Gibbon or Firehole, where your fishing skills will be richly challenged and where taking a dozen trout can be considered a good day.

Yellowstone Park, the largest and oldest National Park in the country offers both types of fishing for visiting anglers - simple and tough. Whatever type you choose, they all have one thing in common - exceptional quality.

The superb angling found in this century-old park rests on two factors: naturally superior trout water to begin with and sound fishing regulations.

Take Yellowstone Lake, for instance. It boggles tourists' minds that they have to throw back all fish over 13 inches and can keep only two small fish under size.

A young Frenchman, who watched me release my 60th trout over 13 inches one afternoon on the southwestern shore of Yellowstone was particularly astonished by this rule.

"In France," he said, "we have to release trout under six inches. Anything bigger, we keep."

Maybe that's why in France you can't catch 60 trout in the one- to two-pound class before lunch.

There is a sound reason for this apparently irrational law. Park fishery biologists feel that the big fish are most important in sustaining a healthy breeding population of cutthroats in the lake and that these trout deserve more protection than the little fellows.

The wisedom of their theory is confirmed again and again as you cast into this magnificent lake surrounded by pine, and spruce-covered mountains. Taking a fish under 13 inches is rare. Most run 15 to 20 inches. Of 110 trout caught one day, only six were under 13 inches. That is trout fishing.

Angling in Yellowstone is a particularly satisfying experience for the Eastern sportsman because the trout populations consist entirely of wild trout. No fish have been stocked in park waters for 20 years. Though only cutthroats are native to this region, established populations of browns, rainbows and brooks are found in various drainages.

The most appealing fishing opportunities for the Washington angler visiting the park are those offered by the natives - the cutthroat trout. Though gullible and perhaps too naive to satisfy the expert trout fisherman for an extended period, the cutthroat's free-rising habits, hard fights and exquisite beauty make him an attractive quarry.

Cutthroats vary widely in color, from pale yellowish-green to a dark grayish-olive. Black spots are sprinkled along the flanks and a red stripe runs down the sides. The checks are deep maroon, almost purple in some specimens, and the characteristic slashes on the underside of the throat are bright reddish-orange.

The Yellowstone River between Canyon and Fishing Bridge offers perhaps the best dry-fly cutthoart trout fishing in the country. A skilled angler can take up to 50 to 100 trout here in a day. Almost every fish nabbed will run between 14 and 20 inches. The fish are robust and will weigh between one and three pounds, with occasional four-pounders turning up in the catch.

The best patterns for taking Yellowstone River cutthroats are the Adams, sizes 12-18, and a gaddis pattern in sizes 14 and 16, tied with an olive rabbit fur body and deer hair laid flat over the top for wings.

This is fun fishing, and occasionally it can get ludicrous. I was casting in one riffle and taking quite a few trout one sunny afternoon when I felt a tapping against my leg. Looking down there was a school of 10 big cutthroat trout at my feet.

Trout like rocks to hold behind in the fast current, and apparently these cutthroats thought I was a rock. For a lark, I dapped the fly over the school and a 17-incher shot up and snatched it. Then another, and another.

When you tire of this easy fishing, try the Gibbon in its meadow stretches. Those who fish the Letort River in Pennsylvania will feel right at home on this fertile little spring creek. It is loaded with canny browns that can frustrate even the most skilled anglers. Hoppers and ants are good patterns here. They fooled browns up to 19 1/2 inches on a wind-whipped day in July.

There is of course, heavy tourist traffic in Yellowstone during the summer. One of the best ways to escape this congestion is to hike up gentle Slough Creek in the northeast corner of the park. Here you'll find hundreds of cutthroats and occasional rainbows willing to sip in your dry flies all day long.

The best advice for families with children who do not fly fish is to bring some clear plastic bubbles and a selection of small drab nymphs in sizes 14-16. Tie the fly a couple feet behind the bubble and cast and retrieve this rig with a spinning outfit. Lures are practically useless in the park.

A large measure of the satisfaction of fishing Yellowstone comes from things other than fish. The air is crips, dry, and almost frighteningly clean to the Eastern urbanite. Temperatures hover in the 70s during the day and drop comfortably into the 40s and 50s at night.

There is no attractive scenery that the sensibilities are overloaded. It's difficult to soak it all in. Skies are postcard blue and acres of purple and yellow wildflowers dance in the breezes.

Wildlife is seen at every turn. Elk graze lazily in the meadows, a bear ambles quietly through the woods, a half-ton moose walks with lanky legs down to feed as you cast for rising trout in the waning sunlight.

Fishing is free in Yellowstone, though a permit must be obtained when you enter the park. There are well designed campgrounds with fees from $2.53. These are all filled by late morning, so plan on arriving between 8 and 10 a.m. to find an open site.

For more information on fishing campsites, and weather at Yellowstone, write Superintendent, Yellowstone National Park, Wyoming 82190.