"The Bear" is one of Robert Frost's sardonic nature poems that purports to be about flora or fauna but in reality provides satiric commentary upon the nature of humanity. Other poems in this vein include "Nothing Gold Can Stay" and "Departmental."

The poem begins by describing a free-roaming bear that powerfully strips a tree of its berries and then lopes across the countryside disregarding rock walls, barbed-wire fences, and trees. Frost then transitions from the bear to mankind with the statement, "The world has room to make a bear feel free; / The universe seems cramped to you and me." The rest of the poem describes the extremes of human endeavor via science (symbolized by the telescope and microscope) and philosophy (represented by "one Greek" and "another Greek").

In this second part of the poem, Frost uses the caged bear as an analogy. We've all seen bears in the zoo, notably polar bears, that keep retracing a circuit from one end of their enclosure to the other or sit in place rocking or twisting methodically. Frost compares humanity's discontented pursuits to the bear's meaningless vacillations.

The best part of this poem is how funny it is. Its humor results first from the ironic contrasting images—comparing the intelligent human with the instinct-driven bear but acknowledging that the bear has a clearer purpose and direction in life (and perhaps more satisfaction).

More humor arises from Frost's wording and clever phrasing. Some examples of his impactful syntax are:

"His mood rejecting all his mind suggests."

"Two instruments of nearly equal hope,
And in conjunction giving quite a spread."

"Between two metaphysical extremes.
He sits back on his fundamental butt..."

In the last example, the juxtaposition of multisyllabic, serious terms with "butt" provides additional comedy.

Finally, Frost employs feminine rhyme, a classic humor approach, in the last couplet. Rhyming the multisyllabic words "pathetic" and "peripatetic" is surprising as well as pleasing to the ear. The ambiguity of the final couplet is also funny: Is the "baggy figure" the bear, one of the Greeks, or the human who represents us all? The ambiguity clinches the analogy: there is little difference between people and caged bears.

"The Bear" represents Frost's skill at providing a tongue-in-cheek look at human foibles after using nature as a springboard.

The question doesn't indicate what kind of analysis should be done and to what extent. I like analyzing a poem's rhyme scheme, rhythm, and meter, so I'll do that with this Frost poem.

Let's start with the consistent part of the poem. It is written in AABBCCDD etc. rhyme scheme. This means that each pair of lines rhymes with each other. A pair of rhymed lines of poetry is called a couplet, so Frost uses couplets in this poem; however, his couplet style is not consistent. Often, couplets will be lines of the same meter. Frost does that in this poem, but he also has couplets in which one line is 11-12 syllables and the other line has a different syllable count.

At the other agreeing with another Greek
Which may be thought, but only so to speak.

Oddly, there is a couplet that visually doesn't look like it rhymes at all.

With lifted snout and eyes (if any) shut
(He almost looks religious but he's not),

A reader could slightly change the pronunciation of "not," and the rhyme would work, and an audience would still know what is being said.

As for the rhythm, the poem is written in the iambic foot. That's not surprising. It's a common rhythm for a lot of poets. That means the words in each line of the poem flow with an unstressed syllable followed by a stressed syllable.

Her next step rocks a boulder on the wall

If the line contains 5 iambic units, then the line is written in a very traditional iambic pentameter. Frost uses this common meter in the poem; however, he definitely doesn't stick with it. There are lines of the poem that contain 11 and even 12 syllables.

The bear puts both arms around the tree above her
And draws it down as if it were a lover