Some Penneys customers are facing an estimated waiting time of up to five hours to book an appointment to shop in stores from Monday.
It comes as businesses and consumers prepare for the easing of restrictions next week.
The retailer, which trades as Primark outside Ireland, says it is experiencing a high volume of traffic.
It says it is using a virtual queue system to monitor the amount of users on the website at the same time.
"This will ensure you have the best possible online experience," it adds.
However a person's position in the queue does not guarantee a booking in a preferred shop.
Its online booking system is live for 'shopping by appointment' between May 10th and 16th, ahead of a full re-opening of stores on May 17th.
Penneys will also have extended opening hours across every store initially, to help reduce queues and spread demand.
This shopper in Dublin told Newstalk: "I'm excited to go to Penneys and get new socks, because they're all covered in holes - and doing a bit of shopping."
Another woman said: "We're going to get to go back to Penneys now as well: socks have become a problem - they're disappearing somewhere between the washing machine and the baskets."
Intercounty travel, religious services, adult sports training and visits to gardens are some of the things being eased from Monday.
Penneys - along with all non-essential retail - will re-open for click-and-collect and for appointments.
Other restrictions easing include numbers attending wedding and funeral services, which will be capped at 50 people.
While public transport will also go back to 50% capacity.
Additional reporting: Andrew Lowth