1756 in Wales

Incumbents

• Lord Lieutenant of North Wales – George Cholmondeley, 3rd Earl of Cholmondeley
• Lord Lieutenant of Glamorgan – Other Windsor, 4th Earl of Plymouth
• Lord Lieutenant of Brecknockshire and Lord Lieutenant of Monmouthshire – Thomas Morgan
• Lord Lieutenant of Cardiganshire – Wilmot Vaughan, 3rd Viscount Lisburne
• Lord Lieutenant of Carmarthenshire – George Rice
• Lord Lieutenant of Denbighshire – Richard Myddelton
• Lord Lieutenant of Pembrokeshire – Sir William Owen, 4th Baronet
• Lord Lieutenant of Radnorshire – William Perry ; Howell Gwynne
• Bishop of Bangor – Zachary Pearce ; John Egerton
• Bishop of Llandaff – Richard Newcome
• Bishop of St Asaph – Robert Hay Drummond
• Bishop of St Davids – Anthony Ellys

Events

• 5 January – An article appears in The New York Mercury, criticising the work of Lewis Evans in identifying boundaries in his General Map of the Middle British Colonies in America.
• Spring – Completion of Britain's longest single-span bridge, William Edwards' Old Bridge, Pontypridd, over the River Taff, at the third attempt.
• Lewis Morris loses his post as collector of tolls at Aberdyfi.

Arts and literature

New books

• Hugh Hughes – Cywydd Galarnadd am ynys Minorca...
• Sion Kadwaladr – ''Einion a Gwenllian''

Music

• Elis Roberts – "Argulus"

Births

• January – Richard Griffiths, industrial pioneer who opened up transport links into the Rhondda
• 7 June – Edward Davies, writer
• 23 June – Thomas Jones, mathematician
• 4 July – John Evans, surgeon and cartographer
• 18 November – Thomas Burgess, Bishop of St David's
• date unknown
• *Thomas Jones of Denbigh, minister and author
• *Simon Lloyd, Methodist preacher

Deaths

• 12 June – Lewis Evans, surveyor, 56?
• 5 August – Sir George Wynne, 1st Baronet, landowner and politician, 56
• 14 September – William Parry, antiquarian and fellow of Jesus College, Oxford, 69
• 23 September – John Talbot, judge and MP for Brecon, about 43/44
• 28 October – Charles Somerset, 4th Duke of Beaufort, 47