A method of elevating a marine platform that is supported by a plurality of hollow metallic leg sections (14, 83) that extend above and below a water line of a body of water, said platform having a deck supported by the leg sections (14, 83), comprising the steps of: a) cutting one of the leg sections (14, 83) at a position next to the water line to provide a cut (42, 43, 90) at a selected elevation; b) attaching a pair of sleeves to the leg section (14, 83) that was cut in step "a", the sleeves being an inner sleeve (24, 29, 95) and an outer sleeve (44, 101); c) attaching a plurality of hydraulic rams (64, 102) to the leg sections (14, 83), each ram (64, 102) having a hollowed cylinder and an extensible push rod (66, 106, 107) and first and second end portions, the rams (64, 102) being attached to the leg section (14, 83) at the end portions, one end portion being attached to the leg section (14, 83) above the cut (42, 43, 90) and not to the deck, and the other end portion being attached to the leg section (14, 83) below the cut (42, 43, 90), and wherein each ram (64, 102) has a retracted and an extended position; d) repeating steps "a" through "b" for the other leg sections (14, 83) of the platform; e) elevating the platform by extending each ram (64, 102) to the extended position; characterised in that: the inner (24, 29, 95) and outer (44, 101) sleeves in step "b" are in telescoping placement, one sleeve inside the other sleeve; the outer sleeve (44, 101) is connected to the leg section (14, 83) on one side of the cut (42, 43, 90); a support ring is connected to the leg section (14, 83) on the other side of the cut (42, 43, 90), the support ring being positioned above the outer sleeve (44,101); and the end portions of the hydraulic rams (64, 102) are respectively connected to the outer sleeve (44, 101) and the support ring. a) cutting one of the leg sections (14, 83) at a position next to the water line to provide a cut (42, 43, 90) at a selected elevation; b) attaching a pair of sleeves to the leg section (14, 83) that was cut in step "a", the sleeves being an inner sleeve (24, 29, 95) and an outer sleeve (44, 101); c) attaching a plurality of hydraulic rams (64, 102) to the leg sections (14, 83), each ram (64, 102) having a hollowed cylinder and an extensible push rod (66, 106, 107) and first and second end portions, the rams (64, 102) being attached to the leg section (14, 83) at the end portions, one end portion being attached to the leg section (14, 83) above the cut (42, 43, 90) and not to the deck, and the other end portion being attached to the leg section (14, 83) below the cut (42, 43, 90), and wherein each ram (64, 102) has a retracted and an extended position; d) repeating steps "a" through "b" for the other leg sections (14, 83) of the platform; e) elevating the platform by extending each ram (64, 102) to the extended position; the inner (24, 29, 95) and outer (44, 101) sleeves in step "b" are in telescoping placement, one sleeve inside the other sleeve; the outer sleeve (44, 101) is connected to the leg section (14, 83) on one side of the cut (42, 43, 90); a support ring is connected to the leg section (14, 83) on the other side of the cut (42, 43, 90), the support ring being positioned above the outer sleeve (44,101); and the end portions of the hydraulic rams (64, 102) are respectively connected to the outer sleeve (44, 101) and the support ring.