i have factory unlocked iphone 3gs. but when i insert sim it shows invalid. any help!!!

Where did you get this "factory unlocked" iPhone? An invalid SIM message usually indicates that the iPhone is not in fact unlocked. If this message just started to appear after you upgraded or restored your iPhone, then your iPhone was in all probability not legitimately unlocked but rather jailbroken and has now been locked back to the original carrier.

Regards.

Again I ask, where did you get this "unlocked" iPhone?

Then it was almost certainly locked to a carrier. If the affiliate selling the iPhone claimed that it was factory unlocked, they probably lied or were mistaken, and you should return the iPhone to them for a refund.