Both boys were born in Crow Tree Road, Bishopwearmouth, Sunderland.
Patrick went to work for his father and worked on Meik's harbours at Burntisland and Bo'ness on the river Forth in Scotland before being asked by Sir Benjamin Baker to be resident engineer (1882-1885) on the foundations and piers of the Forth Rail Bridge (designed by Baker and Sir John Fowler). After this project, he moved to London to set up his own engineering practice.
In 1894, he was joined by his brother Charles and together they worked on a major commission to construct docks and a railway at Port Talbot, followed by an equally ambitious scheme to expand the port of Seaham, officially opened in 1905. The Meiks' expertise saw port and railway designs developed in many parts of the British Empire, including Christmas Island, India, Burma (the Rangoon river training works - where Patrick worked with Sir George Buchanan (engineer)) and Mozambique. The firm was then commissioned to design the Kinlochleven hydroelectric scheme in the Scottish Highlands.
Patrick Meik died in 1910, mourned as "an able and accomplished engineer: whose "kindness of heart and social qualities endeared him to a large circle of friends".