The arrangement comprises a self-climbing installation platform comprising two consecutive decks, a machine room deck suspended from the installation platform and an elevator car suspended from the machine room deck. Each deck, the machine room deck and the car are supported movably with guide means on guide rails and locked and unlocked with locking means to the guide rails and/or to guide rail fixing means. Lifting means powered by a power source move the two decks in relation to each other. The installation platform climbs stepwise along the guide rails by alternatingly locking and unlocking the lower deck and the upper deck to the guide rails and/or to the guide rail fixing means and thereafter raising the unlocked deck.