The Queen is to visit sports stadium Croke Park in Dublin, where 14 spectators were killed by British forces more than 90 years ago.
On her second day in the Republic of Ireland, she will also attend a service honouring Ireland's war dead.
Later at a banquet at Dublin Castle, she will make her only public speech.
She is likely to acknowledge past difficulties, but is unlikely to apologise for past behaviour, BBC royal correspondent Peter Hunt said.
Wednesday will start with a trip to tourist attraction the Guinness Storehouse, but later the Queen will move on to Croke Park in inner city north Dublin, the home of gaelic sports.
The spectators were killed by British forces during the War of Independence in November 1920.
BBC royal correspondent Peter Hunt described it as "the once unimaginable becoming the norm" when the Queen will walk on hallowed nationalist turf at Croke Park.
Soldier memorial
An aspect of history which has been troubling for the Queen's hosts will be touched on when she attends a ceremony to honour the nearly 50,000 Irish soldiers who died in World War I.
For decades, when the focus of admiration was on the rebels who fought and died in the 1916 Easter Rising, the soldiers' contribution went unrecognised.
In the evening at Dublin Castle, which used to be the seat of British rule, the monarch will deliver a speech in the same room where Queen Victoria once dined.
Her first day went smoothly, although there were some protests.
A wreath was laid at the Republic of Ireland's Garden of Remembrance with President Mary McAleese beside her.
The garden, in Dublin, is dedicated to people who fought for Irish independence from Britain.
The visit is one of the country's biggest security operations, with much of the centre of Dublin cordoned off on Tuesday, leaving many streets empty.
Early in the day it emerged that a pipe bomb found on a bus bound for Dublin on Monday had been made safe by the Irish army.
As the Queen laid the wreath, riot police officers jostled with demonstrators at two separate protests on streets several hundred yards from the garden.
The sounds of protesters could be heard during the laying of the wreath and black balloons were released by some demonstrators.
Up to 200 supporters of the Eirigi socialist republican party later retreated to stage a rally nearby.

BBC