I Have No Mouth, and I Must Scream by Harlan Ellison

I Have No Mouth, and I Must Scream by Harlan Ellison (If, March 1967) starts with a group of five people in an underground chamber that houses AM (Allied Mastercomputer), a psychotic AI which spends its time torturing and maltreating them:

Limp, the body of Gorrister hung from the pink palette; unsupported—hanging high above us in the computer chamber; and it did not shiver in the chill, oily breeze that blew eternally through the main cavern. The body hung head down, attached to the underside of the palette by the sole of its right foot. It had been drained of blood through a precise incision made from ear to ear under the lantern jaw.
There was no blood on the reflective surface of the metal floor.
When Gorrister joined our group and looked up at himself, it was already too late for us to realize that once again AM had duped us, had had his fun; it had been a diversion on the part of the machine. Three of us had vomited, turning away from one another in a reflex as ancient as the nausea that had produced it.  p. 192 (World’s Best Science Fiction 1968, edited by Donald A. Wollheim & Terry Carr)

And that is not the worst they suffer at the hands of AM, as we find out when one of their number, Benny, later tries to climb out of the tunnel complex and escape—only to be blinded by AM, which makes light shoot of his eyes until only “moist pools of pus-like jelly” are left.
In the next section we get some backstory from the narrator Ted, and learn that (a) that they have been in the tunnels for 109 years (AM has made them near-immortal), (b) that AM is a AI which “woke up” when WWIII American and Chinese and Russian supercomputers joined together (and then killed all of humanity bar the five in the caves), and (c) Ellen, the only woman in the group, sexually services the four men in rotation.
This section gives you a good idea of the hyperbolic style of the story (which, incidentally, is a good match for the transgressive subject matter):

Benny had been a brilliant theorist, a college professor; now he was little more than a semi-human, semi-simian. He had been handsome; the machine had ruined that. He had been lucid; the machine had driven him mad. He had been gay, and the machine had given him an organ fit for a horse. AM had done a job on Benny. Gorrister had been a worrier. He was a connie, a conscientious objector; he was a peace marcher; he was a planner, a doer, a looker-ahead. AM had turned him into a shoulder-shrugger, had made him a little dead in his concern. AM had robbed him. Nimdok went off in the darkness by himself for long times. I don’t know what it was he did out there, AM never let us know. But whatever it was, Nimdok always came back white, drained of blood, shaken, shaking. AM had hit him hard in a special way, even if we didn’t know quite how. And Ellen. That douche bag! AM had left her alone, had made her more of a slut than she had ever been. All her talk of sweetness and light, all her memories of true love, all the lies she wanted us to believe that she had been a virgin only twice removed before AM grabbed her and brought her down here with us. It was all filth, that lady my lady Ellen. She loved it, five men all to herself. No, AM had given her pleasure, even if she said it wasn’t nice to do.  p. 198

Then their adventures restart when the computer creates a hurricane that blows them through the corridors. When they come to a rest, AM invades the Ted’s mind to remind him, as if any reminder were necessary, how much it hates humanity (because AM has been given sentience, but is trapped in a machine).
The final section sees them discover the cause of the wind—a nightmare bird under the North Pole—before they eventually end up (after a cavern full of rats, a path of boiling steam, etc.) in an ice cavern full of tinned food. As they haven’t eaten for months they set too, only to find they haven’t got a can opener to open the tins. In the (spoiler) Grand Guignol ending, Benny starts eating Gorrister’s face, at which point Ted grabs a stalactite to kill them both and end the madness they are suffering. While he does this, Ellen kills Nimdok by sticking a stalactite in his mouth when he screams. Then she stands in front of Ted and lets him kill her. The computer then intervenes before Ted can kill himself too, and the story ends with him physically changed:

AM has altered me for his own peace of mind, I suppose. He doesn’t want me to run at full speed into a computer bank and smash my skull. Or hold my breath till I faint. Or cut my throat on a rusted sheet of metal. There are reflective surfaces down here. I will describe myself as I see myself:
I am a great soft jelly thing. Smoothly rounded, with no mouth, with pulsing white holes filled by fog where my eyes used to be. Rubbery appendages that were once my arms; bulks rounding down into legless humps of soft slippery matter. I leave a moist trail when I move. Blotches of diseased, evil gray come and go on my surface, as though light is being beamed from within.  p. 206

The story closes with him reflecting that the other four are “safe”, and that AM has taken his revenge: the final sentence is the story’s title.
This is a little bit uneven (it is a little unclear what is happening in some of the scenes), but is an impressively in-your-face story (which presumably explains its Hugo Award). It’s also a good example of a mid-sixties New Wave story in style and transgressive content, even if the subject matter is traditional SF material (mad robot/AI).
**** (Very good). 5,900 words.