The RMT union said about 1,800 members, including train crew and some drivers, were taking action against threatened job cuts and disputes over working conditions and safety.
General secretary Mick Cash said: "RMT will not sit back while nearly 200 members' jobs are under threat."
Virgin Trains said it would be running a full timetable during the strike.
Virgin Trains East Coast, which operates services between London, north-east England and Scotland, said it was making changes to customer-facing roles which would "see a single person take responsibility for the customer experience on our trains".
"This will have no impact on safety, and will result in a better experience for customers," a statement said.
The RMT union claims the measures would lead to job cuts and impact on working conditions and safety measures which currently ensure a guard on every train.
It said nearly 200 jobs were threatened by the cuts and remaining staff would be expected to cover the extra work.
Its members have been instructed not to work any shifts between 00:01 and 23:59 BST on Monday.
General secretary Mick Cash said: "We will also not tolerate the cavalier attitude to safety that is now on show as the company mobilises its scab army of managers."
David Horne, managing director of Virgin Trains East Coast, said: "We have worked hard to ensure there are comprehensive contingency plans in place and I want to reassure our customers that our timetable will be unaffected.
"We're extremely disappointed with the RMT's decision to proceed with strike action when we have given assurances on each point raised by the union.
"On Wednesday, we agreed to the specific concessions set out by the RMT, but despite this they have decided to go ahead with today's walkout."
He said the changes the company was making was part of a "customer-centric revolution".
"With our guarantees that there will be no compulsory redundancies, no impact on safety, and a full timetable in place during today's walkout, this strike is costing RMT members pay for no reason, particularly as the RMT has agreed to hold further talks with us later this week," he said.
Workers on Virgin Trains East Coast have begun a 24-hour strike in a long-running dispute over jobs.