"The Whipping" doesn't have any specific meter like iambic pentameter or trochaic hexameter (yeah, we can't think of any poems that have that last meter, btw). Since it doesn't have any specific meter, it is an example of free verse.
Just to prove to you that it doesn't have any regular meter, let's take a peek at a few different lines. Here's line 2:
is whipping the boy again.
This line is pretty much in iambic trimeter, which means it should contain three (tri- means three) iambs. But if you look closely, you'll notice that there are actually only two iambs, and something else in the middle. That something else is called an anapest, which is two unstressed syllables followed by a stressed syllable. In this case, that's the "-ing the boy" part.
As another example, take line 20:
and the boy sobs in his room.
This line begins with an anapest ("and the"), and concludes with two iambs ("sobs in his room") (it too is a line of trimeter). There's no real common pattern here, and we double-dog dare you to find one anywhere in this poem. Rhythmically, it's just not there.
Now, in addition to having no fixed metrical scheme, "The Whipping" also has no real rhyme scheme either. Okay, technically speaking, it has no end rhymes that we can see (unless there's some funky way of pronouncing the words that we're not familiar with). Just because there's no end rhyme, however, doesn't mean that there isn't any rhyme at all.
So, what other kinds of rhymes are there? Well, a lot of times free verse poems utilize something called internal rhyme, where words within the same line "rhyme" or somehow echo each other. In the first stanza, for example, that short O sound in "woman" is repeated in "neighborhood" and "goodness," while in the second stanza the long I sound pops up all over the place ("wildly," "while," and "spite"). If you wanna get super-duper-technical, you could say that these internal rhymes we've talked about are examples of assonance. Bust that word out at your next party and see it how goes, Shmoopers.
We know what you're thinking. What's the point of this free verse style, this "no rhyme scheme and no meter" deal? Even though Robert Frost once said that writing free verse is like playing tennis with the net down, it does have a purpose. For one, it gives the poet a little more freedom. Think about it like this: what if you came up with an awesome line for this poem you're writing but somehow can't figure out how to make it fit the meter you've chose? Yeah, that would be really annoying, wouldn't it?
With "The Whipping," there's a little more to the story. The poem is almost like a snapshot, a record of the speaker's thoughts as he watches a violent scene unfold in front of him. We know that most people don't actually think in iambic pentameter, or trochaic tetrameter, right? (Okay, maybe Shakespeare did, but that doesn't count.) The absence of any strict formal rules (a defined rhyme scheme and a regular meter), then, makes this poem seem more like a real observation that somebody would make.
Moreover, towards the latter half of the poem, the speaker goes into a sort of stream of consciousness deal where he attempts to describe somebody's memories (either his own or the woman's, it's not clear). Free verse is the perfect type of verse to use in a poem that is exploring the human mind and its highly irregular (and free) succession of thoughts. It's a pretty slick choice there, Mr. Hayden, if we do say so ourselves.