PURPOSE: To obtain the structure of high-medium rise building having sufficient strength against vibration such as earthquake with high efficiency of construction operation on site at low cost.

CONSTITUTION: Housing units 10 and 10A to constitute a housing for first stair are set vertically and horizontally on the first stair of a building. On the units 10 and 10A, housing units 10 and 10A to constitute each stair of the building are stacked up to construct a medium or high rise building by integrating the adjacent housing units 10 and 10A. The rigidity of the units 10A constituting at feast one vertical row of the units 10 and 10A is made higher than that of the other units. Also, a vibration-isolating mechanism is provided for the medium or high rise building.