Robert Glenday was educated in Scotland and came to the Cape Colony in 1892. In 1897 he was employed on irrigation works at Steynsburg. He became a member of the Cape Society of Civil Engineers at or soon after its formation late in 1902 and remained a member to at least 1907. However, by 1903 he had settled in Bloemfontein, Orange River Colony. He investigated and advised on various water and irrigation schemes, one of them in collaboration with James Lyle*. By 1906 he was an associate member of the (British) Institution of Civil Engineers. In July that year he entered the civil service, and in February 1907 was appointed chief engineer of roads, bridges and irrigation for the Orange River Colony and secretary to the Roads Commission.
In December 1904 Glenday read a paper before the Philosophical Society of the Orange River Colony on "Irrigation and its prospects in the Orange River Colony". The paper was published in the society's Transactions (Vol. 1, pp. 29-) for 1903-1907. After briefly considering the history of irrigation in other countries, he dealt with some factors to be considered in planning irrigation, such as rainfall, evaporation, run-off, and crops to be grown. He became a member of the society in 1907.
By 1910 Glenday had also joined the South African Association for the Advancement of Science as a member. When the civil services of the South African territories were combined following the formation of the Union of South Africa in 1910, he retired on pension. However, in October 1911 he was appointed as engineering assistant in the administration of the Cape Province at a remuneration of 30 shillings per day - a post he still held in 1914. During approximately 1915 to 1922 he was the engineer in charge of the builing of Chapmans Peak Drive, a 9 km long spectacularly scenic coastal drive between Hout Bay and Noordhoek.
He was married to Laura Beatrice Glenday, born Hall.