It was perhaps his reading of American poet Walt Whitman that encouraged him to experiment with free verse in works in his native Arabic. But he also drew inspiration from the Jahili (pre-Islamic) and Sufi concept of the poet as a visionary introducing (along with Gibran Kahlil Gibran) two new poetic forms which he called shi'r manthur (free verse) and qasidat al-nathr (prose poem). His first free verse poem was published in 1905 in the magazine Al-Hilal. This new poetry was influential in the Arab world and continued to be so after Rihani's death in 1940. It has been said to be the origin of modern Arabic poetry.
Rihani explored neglected rhythm structures (taken from Arabic form), his stanzas are irregular with lines of different length, no or variable meter (depending on how you define meter) and a non-standard rhyme scheme. Some have compared his style to that of Qur'anic verse. Sadly his poetry, in spite of its revolutionary impact, is hard to find online but here is a sample:
I am the East.
I have philosophies, I have religion, who would exchange them for airplanes.
You can find out more about Ameen Rihanni here http://www.ameenrihani.org/.