The new phones were revealed on Wednesday and opened for pre-orders today. The first phones will arrive on Friday.
Apple encouraged users to pre-order those devices through its online store as well as its app. But as pre-orders opened on Friday, users were hit by a flurry of technical problems.
Customers complained they were unable to load pages or add the new phones to their baskets. Others saw error pages.
Those affected were advised to keep refreshing the pages, or to shut the app and try to order again.
Shipping dates for the new phones have already begun to slip into October and beyond, meaning those affected may have missed their chance to get the new phone on the day it is released.
The new phones were released after a major live-streamed event on Wednesday evening, which also saw the launch of new Apple Watches and AirPods.
Those new Apple Watches immediately opened for pre-order, and will arrive on Friday, 16 September, along with the iPhones.
The new iPhones include a range of features. While the iPhone 14 has relatively limited upgrades, the Pro model brings an always-on display, the removal of the “notch” that hides the cameras and sensors at the top of the phone, and upgraded processors and cameras.
The only new model not to be part of today’s release is the iPhone 14 Plus, which will begin arriving on 7 October.