As the play is about the main character Krapp listening to his younger self speaking freely and unedited about his thoughts, like some kind of diary, Beckett writes the monologues in the stream of consciousness style—that is, a style that aims to replicate the flow of natural speech.
This is partly why the older Krapp criticizes his younger selves so vehemently and why he is at times so embarrassed. He knows his younger selves mean or are striving to mean what they say. For example, look how he joins in with his thirty-nine-year-old self laughing at his self in his twenties:
Hard to believe I was ever that young whelp. The voice! Jesus! And the aspirations! (Brief laugh in which Krapp joins.) And the resolutions! (Brief laugh in which Krapp joins.) To drink less, in particular. (Brief laugh of Krapp alone.)
He is even more disparaging about his thirty-nine-year-old self:
Just been listening to that stupid bastard I took myself for thirty years ago, hard to believe I was ever as bad as that.
All the monologues are written in the stream of consciousness, but perhaps the best example is when Krapp is taking about an old girlfriend. Notice how informal it sounds and how seamlessly it flows from one thought to the other. Just like normal speech.
upper lake, with the punt, bathed off the bank, then pushed out into the stream and drifted. She lay stretched out on the floorboards with her hands under her head and her eyes closed. Sun blazing down, bit of a breeze, water nice and lively. I noticed a scratch on her thigh and asked her how she came by it. Picking gooseberries, she said. I said again I thought it was hopeless and no good going on, and she agreed, without opening her eyes. (Pause.) I asked her to look at me and after a few moments--(pause)--after a few moments she did, but the eyes just slits, because of the glare. I bent over her to get them in the shadow and they opened. (Pause. Low.) Let me in. (Pause.) We drifted in among the flags and stuck. The way they went down, sighing, before the stem! (Pause.) I lay down across her with my face in her breasts and my hand on her. We lay there without moving. But under us all moved, and moved us, gently, up and down, and from side to side.