A mobile offshore drilling unit (MODU) jacking system includes a plurality of hydraulic continuous linear motion motors, preferably comprising a plurality of phased hydraulic piston/cylinder units, that are engaged with a plurality of MODU supporting legs to provide continuous relative motion between the MODU platform and its supporting legs, and to also maintain the MODU platform and MODU supporting legs locked in a stationary relationship. In the preferred jack-up system, the number of hydraulic piston/cylinder units and the number and design of the teeth that are engaged in providing relative motion may be combined to substantially reduce material stresses on the system.