Armstrong originates in the area along the western Scottish borders; the first recorded bearer was Adam Armstrong, pardoned in Carlisle in 1235 for causing another man's death. They were among the most notorious of the riding Border clans, who also included the Elliots, the Grahams and the Johnstons, famous for their lawlessness and plunder. When the power of these clans was savagely broken after 1603 by James I, the Armstrongs scattered, and many migrated to Ulster, where a large number settled in Co. Fermanagh. Even today, Fermanagh is home to the largest concentration of Armstrong families in Ireland, although the name is quite common throughout Ulster, particularly in counties Antrim and Tyrone.

As well as those of Scottish origin, however, a good number of Irish Armstrongs are of Gaelic Irish extraction. Many of the Trin-Laverys of Co. Antrim and the Trainors of counties Tyrone and Monaghan had their surnames mis-translated as Armstrong, from the presence of the Irish for "strong", trean, in their original names.

Armstrong households by county in the Primary Valuation property survey of 1848-64.
Click on a county name for a parish breakdown(paying).
Antrim 131
Armagh 68
Belfast city 64
Carlow 3
Cavan 88
Clare 18
Cork 9
Cork city 3
Derry 41
Donegal 41
Down 74
Dublin 40
Dublin city 46
Fermanagh 421
Galway 7
Kerry 3
Kildare 6
Kilkenny 1
Laois 11
Leitrim 56
Limerick 5
Longford 31
Louth 6
Mayo 38
Meath 24
Monaghan 115
Offaly 49
Roscommon 12
Sligo 64
Tipperary 29
Tyrone 149
Waterford 1
Westmeath 9
Wexford 27
Wicklow 8