He was educated at Elgin Academy and the University of Aberdeen, from which he graduated as a Master of Arts in 1854.
He was one of the three foundation professors at the University of Otago. He held the position of mathematical master for nine years at the Ayr Academy and then a similar position at the Edinburgh Academy. In 1870, Shand was appointed in to the Chair of Mathematics and Natural Philosophy at the University of Otago, and he travelled to New Zealand on the ship Wild Deer in 1871, becoming one of the first three professors at that university.
The dual professorship was divided in 1876, and he opted to retain the Chair of Natural Philosophy, which he kept till his retirement in October 1913.
In 1877 he served on the Royal Commission to enquire into the operation of the University of New Zealand. He sat on the Otago Education Board from 1876 to 1896, and was chairman from 1882 to 1885.
He served on the High Schools Board of Governors from 1878 to 1890 and 1898 to 1904. In 1889 the honorary degree of Doctor of Laws was conferred upon him.
Shand died on 30 November 1914 at Dunedin, about a year after his retirement.
He was a member of the New Zealand Institute and of the Australasian Association for the Advancement of Science. He became a member of the Senate in 1877.