A method for constructing an elevator comprising constructing a movable machine room in the bottom end of a hoistway formed in a building under construction; and thereafter hoisting the movable machine room; and constructing an elevator car in the bottom end of the hoistway below the movable machine room; and providing a counterweight in the bottom end of the hoistway below the movable machine room; connecting the elevator car and the counterweight with a suspension roping; and thereafter hoisting the movable machine room to a first transport position; and thereafter mounting the movable machine room to the first transport position in the hoistway vertically supported on stationary structures; and thereafter using the elevator car for transporting passengers and/or goods below the movable machine room while the movable machine room is mounted in said first transport position; and thereafter hoisting the movable machine room upwards to a second transport position; wherein the second transport position is higher than said first transport position; and thereafter mounting the movable machine room to the second transport position in the hoistway vertically supported on stationary structures; and thereafter using the elevator car for transporting passengers and/or goods below the movable machine room while the movable machine room is mounted in said second position, characterised in that said constructing a movable machine room comprises transporting into the bottom end of the hoistway plurality of prefabricated sub modules, and connecting the plurality of prefabricated sub modules to each other in the bottom end of the hoistway, wherein said plurality of prefabricated sub modules comprises a first prefabricated sub module comprising a support platform of a hoisting machine, the support platform comprising one or more releasable mounting mechanisms installed thereon for releasably mounting the moveable machine room in the hoistway, possibly also a premounted hoisting machine; and/or a second prefabricated sub module comprising a working platform forming a roof of the moveable machine room and comprising handrails; and/or at least one third prefabricated sub module suitable for being mounted between the first and second module (41,42) for coupling these to each other. constructing a movable machine room in the bottom end of a hoistway formed in a building under construction; and thereafter hoisting the movable machine room; and constructing an elevator car in the bottom end of the hoistway below the movable machine room; and providing a counterweight in the bottom end of the hoistway below the movable machine room; connecting the elevator car and the counterweight with a suspension roping; and thereafter hoisting the movable machine room to a first transport position; and thereafter mounting the movable machine room to the first transport position in the hoistway vertically supported on stationary structures; and thereafter using the elevator car for transporting passengers and/or goods below the movable machine room while the movable machine room is mounted in said first transport position; and thereafter hoisting the movable machine room upwards to a second transport position; wherein the second transport position is higher than said first transport position; and thereafter mounting the movable machine room to the second transport position in the hoistway vertically supported on stationary structures; and thereafter using the elevator car for transporting passengers and/or goods below the movable machine room while the movable machine room is mounted in said second position, characterised in that said constructing a movable machine room comprises transporting into the bottom end of the hoistway plurality of prefabricated sub modules, and connecting the plurality of prefabricated sub modules to each other in the bottom end of the hoistway, wherein said plurality of prefabricated sub modules comprises a first prefabricated sub module comprising a support platform of a hoisting machine, the support platform comprising one or more releasable mounting mechanisms installed thereon for releasably mounting the moveable machine room in the hoistway, possibly also a premounted hoisting machine; and/or a second prefabricated sub module comprising a working platform forming a roof of the moveable machine room and comprising handrails; and/or at least one third prefabricated sub module suitable for being mounted between the first and second module (41,42) for coupling these to each other.