Eight ships of the Royal Navy have been named HMS Ajax after the Greek hero Ajax:
- HMS Ajax was a 74-gun third-rate ship of the line launched in 1767 and sold in 1785.
- HMS Ajax was a 74-gun third rate launched in 1798. She fought at the Battle of Trafalgar in 1805 and was burned by accident in 1807.
- HMS Ajax was a 74-gun third rate launched in 1809. She was converted to screw propulsion in 1846 and broken up in 1864.
- HMS Ajax was a 78-gun third rate launched in 1835 as HMS Vanguard. She was renamed HMS Ajax in 1867 and was broken up in 1875.
- HMS Ajax was an Ajax-class ironclad battleship launched in 1880 and sold in 1904.
- HMS Ajax was a King George V-class battleship launched in 1912 and broken up in 1926.
- HMS Ajax was a Leander-class light cruiser launched in 1934. She took part in the Battle of the River Plate and was broken up in 1949.
- HMS Ajax was a Leander-class frigate launched in 1962 and broken up in 1988.
- HMS Ajax is planned as the seventh Astute-class submarine.