Stevens doesn’t write a lot of poems as structured as this one. Maybe it has to do with the fact that "Sunday Morning" is one of the first poems he published: a lot of poets start out writing in traditional forms, and then become more experimental. Whatever the reason, this poem is very neat and organized, like a room where everything is in the right place. It has eight stanzas of 15 lines each, which is one line longer than the standard length of a sonnet. The stanzas don’t rhyme, however, so they can’t be called sonnets.
They are written in blank verse, which is the meter that Shakespeare used throughout most of his plays. It just means that, although the lines don’t rhyme, they all have the same meter. Like Shakespeare’s verse, Stevens’s blank verse lines have ten syllables (called "beats") and are written in iambic pentameter, which means that every other beat in the line has an accent. This is just a general rule, however. The first line of stanza II is pretty typical: "Why should she give her boun-ty to the dead." If anything, Stevens is even more consistent than Shakespeare in giving each line exactly ten beats. Can you find any lines in the poem that don’t have ten? This strict pattern is probably the reason that some lines are so difficult to understand: it takes a lot of planning to write in perfect blank verse.