Poetry is relatively common in Egyptian culture. Many examples of Ancient Egyptian poetry has been found. Most I have read rely on metaphor and similes for description and effect. I have only seen one of these in the original Egyptian so I am not really sure if rhyming was common. Of course, translating into English the rhyming patterns would be lost. One of my favorite Ancient Egyptian poems is the following. It is a love sonnet/poem of a sort that says a lot about Egyptian ideals of beauty.
She looks like the morning star,
Rising at the beginning of the year.
Shining bright, fair of skin.
Lovely is the look in her eyes.
Sweet is the speech of her lips.
She has not a word too much.
Upright neck, shining breasts,
Her hair like real lapiz lazuli.
Her arms are gold, her fingers like lotus buds.
Heavy thighs, narrow waist,
Her legs parade her beauty.
With graceful step she treads the ground
And captures my heart by her movements.
She causes all men's necks to turn to see her.
Joy has he whom she embraces.
When she walks abroad she is like the Eye of the Sun.
-Old Kingdom Poem.
I really love the way this reads. You could imagine a man in any time period writing something about a woman he loves with similar words to these ones. That is something I found reading Ancient Egyptian poems is that the content seems to be those things that every age and person thinks about.
Another very interesting love poem. This one I am unsure of the time period but I believe it is New Kingdom.
I wish I were your mirror
so that you always looked at me.
I wish I were your garment
so that you would always wear me.
I wish I were the water that washes your body.
I wish I were the unguent,
that I could annoit you.
And the band around your breasts,
and the beads around your neck.
I wish I were your sandal
So that I may always walk with you.
If you want to learn more there is an awesome piece about Egyptian poetry here on National Geographic's website.
There is also a much longer love poem to be found here.
Google books also has a book available. I have yet to read this one titled Reading Ancient Egyptian Poetry by R.B. Parkinson.