Before you submit your poems, understand that some publications do not accept already published work. Another thing, most of them have a review process and your poem may be accepted or rejected.
Here are the 30 companies.
The Three Penny Review: they only accept short poems (100 words or less) that have not been previously published. They pay $200.
The Boulevard: you can send a maximum of five unpublished poems in one submission. They pay $25 to $250.
Arc Poetry Magazine: you can submit up to three poems with every submission. They pay $50 per page.
Chicken Soup for the Soul: these publishers are asking for poems to publish in upcoming books. They pay $200.
EPOCH: you can submit your poem in any form but only five poems at a time. They pay $50+.
Ploughshares: feel free to submit a poem of between 1-5 pages. They pay $45+.
The Southern Review: they accept a maximum of five poems per submission or 15 pages. They pay $25 to $200.
The Capilano Review: the maximum is five pages. They pay $50 to $150.
AGNI: they accept a maximum of five poems with every submission. They pay $20 and sometimes more.
U.S Kids Magazine: this publication is currently accepting Humpty Dumpty submissions. The pay is $25+.
Orion Magazine: this is a magazine about nature and accepts related poems. The pay is $100.
New Myths: all poems should have a fantasy or science fiction element. They accept five poems at a time. The pay is 1.5 cents per word.
SubTropics: your work should be unpublished and you can only submit four poems at a time. They pay $100.
Willow Springs: you can submit a maximum of six poems at once. They pay $20.
The Sun Magazine: they pay $100 to $200.
Alaska Quarterly Review: you can submit a maximum of 20 pages. They pay $10 to $50.
Blue Mountain Arts: they do not limit the number of poems you should send in. They pay $100 to $350.
Black Warrior Review: it is a publication of the University of Alabama.
Rattle: these ones love unique poems. They pay $50 to $100.
Grain Magazine: submitted poems are limited to six pages. They pay $50 to $250.
The Iowa Review: they pay $1.50 per line.
FunforKidz: they are currently accepting submissions for the Hopscotch magazine. They pay $10+.
The Colorado Review: you can submit a poem in any style. They pay $30+.
VQR: any kind of poem is accepted here. They pay $200 and you can send a maximum of 4 poems.
Iron Horse Review: a single submission is limited to 3-5 poems. They pay $50.
Poetry Foundation: you can only submit four poems at a time. They pay $10 per line.
The Nashville Review: you are allowed to be experimental in your writing. They pay $25.
Leading Edge Magazine: the theme is limited to fantasy or science fiction. They pay $5 to $20.
Slice Magazine: you can only submit unpublished poems. They pay $75.
CrazyHorse: all genres are accepted. They pay $20 to $200.