Earlier today, T-Mobile revealed that its original Samsung Galaxy S4 launch date has been pushed back from April 24 to April 29. The carrier blamed “an unexpected delay with inventory deliveries” as the cause.

Now, it seems that T-Mobile’s supply difficulties were a sign of things to come.

Samsung has issued a statement to Bloomberg making it clear that supplies of its new flagship Android smartphone will be short for weeks after its release.

The statement:

“Due to overwhelming global demand of Galaxy S4, the initial supply may be limited. We expect to fulfill inventory to meet demands in the coming weeks.”

Pre-orders for the Galaxy S4 are already being taken by AT&T, Sprint, U.S. Cellular and some retail locations. (Consumers might want to steer clear of pre-ordering at Best Buy, though, as the store has a history of overbooking smartphone pre-orders.)

Over the past two years, the Galaxy S series has begun to dominate the Android landscape as the only Android smartphones that regularly put up sales numbers even in the ballpark of Apple’s iPhone sales. Being unable to meet high demand is a challenge that Apple has dealt with for years now, and one that Samsung will have to contend with now that it is Apple’s largest rival. Though Samsung is the largest manufacturer of smartphones in the world, even its prodigious manufacturing capabilities can’t keep up with demand for the next Galaxy-branded smartphone.