A jacking method and apparatus for a heavily loaded platform includes hydraulic continuous linear motion motors, preferably comprising a plurality of phased hydraulic piston/cylinder units, that are engaged to drive the heavily loaded platform to provide relative motion of the platform with respect to a platform support, and to also hold the platform in a selected stationary position. 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.