BUS Eireann has warned several services are not operating this morning due to the industrial action.
They include some bus journeys from Belfast, Letterkenny and Derry to Dublin, Kells to DCU, and Dublin Airport to Kells and Wicklow.
Limerick-Dublin services are not operating while services in Drogheda, Dundalk, Monaghan and Cavan are also expected to be disrupted.
In total, up to 50,000 passengers are bracing themselves for travel chaos today as bus drivers go on strike.
Bus Eireann warned there would be disruption to services nationwide when members of the National Bus and Rail Union (NBRU) picket depots, including Busaras in Dublin.
The company revealed it is not yet known if other staff, including members of Siptu who are also being balloted for industrial action, will refuse to pass picket lines, adding to disruptions.
It advised customers to visit buseireann.ie for updates in the coming days. Translink has already confirmed that several cross-border coach services will be affected until further notice.
The strike, which centres on a row over payroll savings of five million euro, is expected to cost Bus Eireann 200,000 euro a day.
Approximately 50,000 customers usually travel on routes across the country on a Sunday.
Both sides had maintained they were available for talks in recent days, but no contact was made between the parties.
Michael Faherty, NBRU general secretary, said he has sympathy for the travelling public but claimed the bus firm had forced the action by implementing a cost-cutting plan which he described as a breach of contract of employment.
But the bus firm said it has not received any credible and viable alternatives from the trade unions that will provide the same level of savings needed to keep staffing and service levels.
Bus Eireann employs 2,500 people, with the NBRU representing 1,000 of the workforce.
Its members voted to reject cost-cutting recommendations from the Labour Court, which they claim could see some workers lose up to 4,000 euro a year in pay.
It had backed a 20% cut to a range of allowance and expense payments, a reduction of overtime rates, longer working hours and a cut in shift payments.
The Government has also warned the bus firm, which is supported by the State, lost 27 million euro (£23 million) over the last five years and would not be financially viable if it does not impose cuts.
The Socialist Party has called on members of Siptu, which will know the result of its ballot on Thursday, and the Transport Salaried Staffs' Association (TSSA) to join in solidarity by not crossing the picket lines.