More than 50,000 railway workers will walk out for 24 hours at a time on June 21, 23 and 25 in what the RMT says is the biggest dispute on the network since 1989.
RMT members on London Underground are also striking on June 21 in a separate dispute on pensions and job losses.
The union is blaming “the inability of the rail employers to come to a negotiated settlement with RMT” on the Network Rail dispute.
The company said it is continuing discussions on pay to attempt to avoid the action.
The action is over pay talks and a demand by the union of a guarantee of no compulsory redundancies in any job losses when the firm makes £1-2bn of cuts. It warns that further job losses will impact safety on the network.
A ballot of members resulted in 89pc voting for strike action on a 71pc turnout.
Andrew Haines, Network Rail’s chief executive, said: “We continue to meet with our trades unions to discuss their pay concerns and we’re doing everything we can to avoid strike action on the railway.
“We know that the cost of living has increased and we want to give our people a pay rise but the RMT must recognise we are a public body and any pay increase has to be affordable for taxpayers and passengers.
“Travel habits have changed forever and the railway must change as well. We cannot expect to take more than our fair share of public funds and so we must modernise our industry to put it on a sound financial footing for the future.
“Failure to modernise will only lead to industry decline and more job losses in the long run.
“There are a few weeks until the first strike is planned. We will use this time to keep talking to our unions and, through compromise and common sense on both sides, we hope to find a solution and avoid the damage that strike action would cause all involved.”
RMT general secretary Mick Lynch said: “Railway workers have been treated appallingly and despite our best efforts in negotiations, the rail industry with the support of the government has failed to take their concerns seriously.
“We have a cost-of-living crisis and it is unacceptable for railway workers to either lose their jobs or face another year of a pay freeze when inflation is at 11.1pc and rising.
“Our union will now embark on a sustained campaign of industrial action which will shut down the railway system.
“Rail companies are making at least £500m a year in profits, whilst fat cat rail bosses have been paid millions during the Covid-19 pandemic.
“This unfairness is fuelling our members’ anger and their determination to win a fair settlement.
“RMT is open to meaningful negotiations with rail bosses and ministers but they will need to come up with new proposals to prevent months of disruption on our railways.”