There are still some slots available for the three midlands stores.
An online portal has opened for people to book a time to go shopping at Penneys.
From Monday, the store opens by appointment-only before a full reopening on May 17th.
The website opened at 10am with some customers already in a queue of an hour.
There are still slots available at the midlands stores in Athlone, Mullingar and Portlaoise.
Penneys will have extended opening hours across every store to cope with demand and reduce queues.