How to complete billing address when we don't have a zip code

Please advise...
I have tried doing some online ordering with USA companies to be shipped to USA addresses.  But, when I have to complete my billing address, I have nothing to put in the zip code field.  If I leave it blank, the information is not accepted.  If I enter all zeros, the information is not accepted.
Please, can someone tell me how to over come this obstacle?
I am eager to hear from you.
Thank you.
Lani

Use the PO Box number

Just put the PO number in the zip code field?

Yes - works for me, no prob

thank you.  I will give it a try.