After showing a talent for drawing and design Ritchie (sometimes called Alexander Handyside Ritchie) was sent to the Edinburgh school of art and, thanks to the sponsorship of the fifth duke of Buccleuch, he obtained a place at the Edinburgh studio of Samuel Joseph (whose work also features in the College's collection). This was followed by a period at the Trustees’ School of Design, Edinburgh, and a period in London and on the continent, which included time studying under the Danish sculptor Bertel Thorvaldsen.
By 1842 Ritchie had established a studio in Edinburgh as he began to gain recognition as a portrait sculptor in the neo-classicist style. Ritchie experienced his greatest success during the 1840s and 1850s. It was in this period that he worked on architectural decoration with notable Scottish architects, such as Thomas Hamilton who designed the College’s premises at Queen Street. He also worked with David Rhind on the Scottish Life Association Building in Edinburgh and in 1848 he was employed by the English sculptor, John Thomas, to carry out decorative work for the Houses of Parliament in London – this included the carved statues of Eustace de Vesci and William de Mowbray.