Around 100 of its delivery offices, including Aberdeen, Dundee, Edinburgh and Glasgow, will open this weekend.
1600 Post Office branches will also open on Sunday as part of a pilot.
The company says the initiative is designed to make it easier for online shoppers not at home during the day to get their parcels.
Royal Mail's network of around 1, 400 delivery offices is currently open six days a week.
Rob Jenson, Royal Mail Operations Director said:
'We are continuing to be more customer responsive and provide more options for people to receive items they have ordered online.
'I am delighted to pilot Sunday afternoon opening at around 100 of our delivery offices across the UK with the highest parcel volumes including delivery offices in Aberdeen, Dundee, Edinburgh, Glasgow and Inverness.'
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