Alexander Cullen was born in Hamilton on 9 April 1892, youngest son of Alexander Cullen and his wife Barbara Rodger. He was educated at Hamilton Academy and Glasgow High School, and attended classes at Glasgow School of Art from September 1910, receiving his architectural training in his father's firm of Cullen, Lochhead & Brown from January 1911 and also studying at the Royal Technical College under Eugène Bourdon. In July 1914 he undertook a sketching and measuring tour of Ely, Cambridge, Lincoln and York. He passed the qualifying exam in Glasgow in March 1915 and soon thereafter was commisssioned in the King's Own Scottish Borderers, subsequently transferred to the Machine Gun Corps, serving in France until the end of the war. He made further measured drawing visits, to Arras in October 1916, to Amiens in March 1917 and to Chalons-sur-Marne in October 1917.

On returning from war in 1919 he rejoined Cullen, Lochhead & Brown as an assistant. He passed the qualifying exam in 1920 and was admitted ARIBA in the same year, his proposers being James Lochhead, John Keppie and John Watson. He made a study trip to Canterbury in 1922 and either from choice or necessity he left Cullen, Lochhead & Brown's at the end of that year. On 1 January 1923 he commenced practice in Hamilton in competition with them, shortly thereafter winning the competition for Glasgow High School War Memorial Sports Pavilion. Professor W J Smith who was a contemporary at Glasgow School of Art and Royal College described his practice as having 'flourished' and during this period he carried out commissions for the British Linen Bank, Messrs Colvilles and local authorities. No work is at present recorded after 1931 but much of his work at this time may have related to town planning as he obtained the RIBA Diploma in Town Planning with distinction and passed the external examinations of the Town Planning Institute and the Royal Institute of Chartered Surveyors, and was for a time Chairman of the Scottish branch of the Town Planning Institute.

Cullen was made a Fellow of the Surveyors' Institution in 1925, a Fellow of the Society of Antiquaries of Scotland in 1924, a Fellow of the Royal Incorporation of Architects in Scotland in 1929, and was admitted FRIBA in early 1930, his proposers being John Keppie, William Brown Whitie and Andrew Balfour. He completed the work in hand of Thomas Spiers Fraser, a former partner in the Cullen, Lochhead & Brown practice who had likewise set up independent practice in Hamilton, after the latter's death in October 1934, although none of these works has yet been identified. In 1936 he married Margaret Watt, daughter of W H Watt.

Between the wars Cullen served in the Territorial Army. When war was declared in September 1939 Cullen became a Lieutenant-Colonel commanding the 6th Battalion of the Cameronians and again served in France bringing his battalion home safely from Cherbourg in 1941 for which his services were awarded with an OBE.

After the war Cullen was only briefly in private practice being appointed in 1946 County Architect and Planning Officer for Invernessshire, a post which he held until his retirement at the age of sixty four, ten years later. Despite post-war restrictions his local housing received a Saltire Award. The RIBA Kalendar of 1950-51 records that at that date he was OBE, TD, FRICS, FRSE, MTPI, FSA (Scot) and that he had been awarded RIBA Distinction and the RIBA Diploma in Town Planning.

Cullen resumed private practice, now based in Inverness, after his retirement but throughout his Inverness years he retained connections with the Glasgow area as a governor of the Royal College and of Glasgow School of Art until 1958. He died on 7 November 1963.

Information courtesy of Dictionary of Scottish Architects.