Additional staff are reported to have been brought in to speed up the process, which is expected to go on for 24 hours.
The Egypt authorities said the priority will be given to students, the sick, people working abroad, the elderly, women and children.
Around 200 Gazans were allowed into Egypt on Wednesday, but the border was closed when hundreds more tried to force their way across, throwing stones at Egyptian border guards, who used water cannons to disperse the angry crowd.
The clashes came despite Israel's move to reopen crossings Wednesday morning to allow for essential supplies through, previously suspended following militant rocket attacks.
In May, several hundred Palestinians were allowed into Egypt through the Rafah crossing for medical treatment, with priority given to the elderly and heart and cancer patients.
Under international agreements, the opening of Rafah can only be sanctioned by Israel with the participation of European Union observers.
Thousands of Gaza residents flooded into Egypt to buy food, fuel, and essential supplies when Palestinian militants blew up sections of the wall at the Rafah crossing in January. It took the Egyptian authorities about two weeks to restore order and secure the border.