Elizabeth Stirling (died 1579) was the second daughter of Sir James Stirling of Stirling Keir (died 1588) by his second marriage. In 1572 she married John Napier of Merchiston (1550-1617), by whom she had two children. Her son, Archibald, became Treasurer-Depute of Scotland and was created Lord Napier of Merchiston in May, 1627.
Her husband devoted his life to agriculture, Protestant theology, scientific investigation and mathematics. In 1594, his Plain Discovery of the whole Revelation of St. John was published; it was an anti-Catholic polemic of enormous influence. However, his most important work was in the development of arithmetic and algebra, which led to 'his discovery of the correspondence between arithmetical and geometrical progression and the logarithmic canon, which after years of intense study he founded upon it,' (Douglas).