Men’s college basketball observers appreciate the nostalgia that Kentucky’s Oscar Tshiebwe and Illinois’ Kofi Cockburn conjure just as much as they value their mastery in the post.

Those who face the two players, who are widely recognized as being among the nation’s most talented bigs, have said that there is little they can do to impede them in the paint: They’re too big, too strong, too skilled for opponents to do anything but watch as they gobble up rebounds, score at will and secure extra possessions for their teams.

Cockburn, a 7-foot junior center, has led Illinois to a No. 4 seed in the N.C.A.A. tournament and is the only player in Division I to average more than 20 points and 10 rebounds per game. Tshiebwe, a 6-foot-9 junior forward, is a favorite to win the Naismith Trophy, given to college basketball’s best player, and is the leading scorer for second-seeded Kentucky.

In an era of hoops in which teams are spacing the floor and prioritizing the 3-point shot, especially at the pro level, Tshiebwe and Cockburn are reminders of what the game used to be. The two have combined for one career 3-point attempt, and both make the most impact with power moves near the basket.

“Some of it may not be all that glorious, and you don’t talk about it as much,” said Ben Sisson, a forward for Kentucky Wesleyan College, a Division II program the Wildcats played in an exhibition in October, “but it’s just as impactful as any other trait you could have in your game.”

In his lone season at Kentucky, Tshiebwe, who transferred to the program from West Virginia, is averaging 17.0 points and 15.1 rebounds per game heading into the Wildcats’ tournament opener against 15th-seeded St. Peter’s on Thursday. At 255 pounds, Tshiebwe’s physicality, strength and rebounding ability make him almost too much for one person to handle, so teams have gone into games knowing they have to double- and triple-team him.

“He’s almost like a law, a natural law,” said Patric Young, a center for Florida from 2010-14. “There’s the natural law of gravity. And the natural law of Oscar Tshiebwe is that he’s going to put 15 and 15 up on you. It’s just a matter of how he’s going to do it.”

Tshiebwe has grabbed nearly 500 total rebounds this season, anchoring a Kentucky team that finished last season with its worst winning percentage in more than 30 years. Now, the Wildcats are in title contention.

Tshiebwe started the season with 20 rebounds against Duke. In a December home game against Western Kentucky, he recorded 28 rebounds — more than the entire Hilltoppers team, and a single-game record in Rupp Arena.

When asked about the record after the game, Tshiebwe said: “When I stop fighting is when the time is up. The game is over. That’s when I stop fighting.”

His ability to play with the same energy throughout the 31.5 minutes he averages as he corrals missed shots on both ends of the floor tires out his opponents, who are constantly fighting for rebounds against his big frame.

“He takes a toll on your body throughout the game,” said Darius Days, a power forward at Louisiana State, which plays Iowa State in the N.C.A.A. tournament on Friday. “At the last six minutes of the game, you’re just dead tired and you’re like, wow, he’s continuing to go to the glass.”

In Kentucky’s loss to Tennessee in the Southeastern Conference tournament, Tshiebwe recorded his 15th straight double-double.

“When you would hit him, he wouldn’t move, but as soon as he would try to move you, there’s nothing you could do about it,” Sisson said. “He was just going to move you wherever he wanted,.”

He added: “He’s like a bulldozer with arms.”

In a time when big men have been expected to adopt an outside shot, Cockburn’s knack for inside scoring is both antiquated and extremely effective. He has made over 59 percent of his shots and averaged 20.0 points and 10.5 rebounds per game in conference play in a tough Big Ten.

Cockburn’s size — 285 pounds — draws double takes. And then, double teams.

“Kofi’s going to get his,” said Trayce Jackson-Davis, a forward for Indiana, which beat Illinois in the Big Ten tournament and won its First Four game Wednesday against Wyoming behind Jackson-Davis’s 29 points. “He’s a great player, he’s an all-American. But at the same time, we knew that we were going to try to slow him down.”

Teams have resorted to intensifying their physicality when they play Cockburn to slow him down, clobbering and hacking at him so much in the paint that Illinois Coach Brad Underwood once referred to him as the “most abused player in college basketball.”

In a win over Rutgers early in the season, Cockburn used his left arm to fend off a defender as he snatched a rebound off a missed 3-pointer with his right hand and dunked one-handed. When Illinois traveled to Rutgers a couple months later, Cockburn knocked a pair of defenders off him with his shoulders, dunked and drew a foul in the same play.

After No. 1 Illinois was upset in the second round of the tournament by eighth-seeded Loyola Chicago last year, Cockburn tested the N.B.A. waters before returning to school. Now, he could lead Illinois to its first deep run in the tournament in almost 20 years.

“It’s what makes March great,” Underwood said. “You can elevate. You can make yourself legendary in March. And he’s got that opportunity."