Ahead of his title defence, Clarke described the rough as “brutal”, while Woods, a three-time winner of the Claret Jug, described it as “inescapable” after his practice round.
Northern Irishman Clarke said the long, lush grass was a problem in certain areas and predicted some players would lose balls this week.
Championship organisers the R&A insist, however, the course is in the best possible condition it can be.
“There are a few patches out there where it’s just absolutely brutal,” said Clarke.
“The grass is a little bit thicker than what you normally find on a links golf course. It’s really, really tough.
“If you start spraying the ball around this week, you might as well go home.
“Obviously, if you start missing the fairways there you’re really going to struggle so it’s a big challenge.
“There’s a really huge premium on accuracy this week. There’s no chance coming out of this rough at all.
“There could be some lost balls in there, even with spotters and everything.”
When asked about the testing conditions, Woods was quoted as saying: “Oh my God. It’s just that you can’t get out of it. The bottom six inches is so lush.
“The wispy stuff, we’ve always faced that at every British Open. But that bottom six inches, in some places it’s almost unplayable. I’ve never seen the rough this high or thick and dense.”
The R&A blamed unprecedented weather conditions for hampering preparations over the last few months and claim they have canvassed opinion from several professionals who are satisfied with the course.
“The feedback we have had from a large enough body of players to be satisfied that they represent the field is that it is fair and well set up,” said R&A communications director Malcolm Booth.
“A large number of players have expressed how pleased they are with the course set-up, which seems to be very positive.
“The weather we have had, unprecedented in this country, means there has been a lot of moisture and rain which, combined with at least some summer heat, has led the rough to being very thick in places.
“That in itself is not unprecedented at an Open Championship – Muirfield in particular gets very thick rough – so we are pleased with the course set-up.
“The fairways are suitably scaled to allow a generous landing area if you are hitting the right club off the tee.
“The weather will keep the fairways softer, too, so things aren’t going to be kicking off fairways with quite the force they would have been doing at Hoylake in 2006.”
Booth said there had been no alterations to the course as a result of the bad weather and they did not plan to make any at this late stage.
He was also confident the non-golf areas would stand up to the weather, although he admitted more heavy rainfall would put a strain on the course inside and outside the ropes.
“I believe it is set up the same way and I don’t think, with the feedback we’ve had, there is any need to make any changes. The water table is pretty high, which is a point for some mild concern at this stage and we hope we don’t get absolute torrential downpours in the next few days,” he added.
“We are reasonably okay at the moment and the course is standing up pretty well given the huge amount of rain which has fallen.
“The tented village areas, if there is sustained rain for three or four days, could become a bit muddy and not as well presented as we would like but still perfectly navigable for spectators.
“Car parking is a challenge but we have a number of good car parks which are on high ground or where it drains pretty well so, from an operational point of view, we are in pretty good shape.
“However, very heavy rain over three or four days will make it more difficult than if we don’t get that kind of weather. We advise spectators to bring waterproofs and sensible shoes.”
As the world’s greatest golfers gathered to try to emulate his 1969 victory on the Lancashire links, Tony Jacklin told them not to complain.
“No matter how unplayable it is somebody will win,” said the 68-year-old, who returns to competition at Turnberry next week in the Senior British Open.
“You really don’t get the guys who are in with a shout complaining about conditions.
“I remember Hazeltine (scene of his runaway victory in the 1970 US Open), Dave Hill said all it needed was a dozen cows and a couple of tractors.”
Hill came second, seven strokes back.
“Golf courses are to be played. The rough was high at Muirfield in 1966 when Nicklaus won – they had two stewards on the left and right of every hole.
“He drove with a one-iron all week. Tiger (Woods) won at Hoylake with a one-iron all week.
“Somebody will figure it out and get it done. It’s just getting your head round it and getting on with it. Whingeing won’t get it.
“Nicklaus said to me that he always thought majors were the easiest ones to win because 95 per cent of the guys didn’t think they could do it.”
Jacklin remains the last English winner of The Open in England – Sir Nick Faldo’s three victories all came in Scotland – but he believes Lee Westwood and Luke Donald both have a good chance this week.
Of the pair, he favours Westwood because of his straight driving.
“You cannot get out of the fact that it’s controlling the golf ball that wins you major championships and that’s the examination,” he said.