The Rail, Maritime and Transport union, which has been striking since February, announced fresh industrial action last week after talks over pay and redundancies fell through.
The strikes have been organised for Tuesday 21, Thursday 23 and Saturday June 25 with all passengers urged to seek alternative modes of transport for their journey.
The industrial action falls on the same day as the Armed Forces Day national event in Scarborough, which is expected to attract more than 200,000 visitors to the town over the weekend.
TransPennine Express said an amended timetable will be in place and that there will also be significant disruption on Wednesday 22 and Friday June 24.
Kathryn O'Brien, Customer Experience Director at TransPennine Express, said: "Due to the RMT action we will only be able to operate around 10 per cent of our usual daily services.
"Alongside other operators, we simply won't be able to provide journeys for the tens of thousands of customers who would normally rely on us and any services we are able to run will be extremely busy.
"It's extremely disappointing that RMT has chosen to take strike action which will not only cause significant disruption for our customers but will also damage the recovery of the rail industry."
Network Rail said about half of all rail lines across the country will be closed.
TransPennine Express said it is waiting for confirmation on ticket acceptance for other travel providers and will publish the confirmed details on its website.
It said passengers' tickets will be valid for travel on the day prior and two days after any strike action and anyone who chooses not to travel will be entitled to a full refund.