The invention relates to an elevator arrangement, comprising a hoistway one or more vertically oriented guide rail lines in the hoistway for guiding vertical movement of one or more movable elevator units, and one or more movable elevator units mounted in the hoistway vertically movably along one or more guide rail lines, including at least an elevator car, preferably also a counterweight, and a hoisting roping; a movable support structure mounted in the hoistway for supporting said one or more movable elevator units below it via said hoisting roping, and a hoisting machine on the movable support structure for moving the hoisting roping, for thereby moving said one or more movable elevator units. Said movable support structure comprises a body portion, and a shelf structure projecting laterally from the body portion, and the hoisting machine is mounted on the shelf structure. The invention also relates to a method for constructing an elevator implementing the arrangement.