To provide an inexpensive damper of a simple structure which damps the vibration of a building construction over a wide range from small to large vibrations caused by wind and earthquakes.

This damper comprises a vibration-absorbing rubber member 11, in which vibration-absorbing rubber 11c made by high-damping rubber is sandwiched between an inner plate 11a and an outer plate 11b, and a low-yield- strength member 12 formed of dead soft steel having a lower yielding point than steels for a building construction, such as columns, beams, and braces, and through holes (a) of the same diameter are bored in the mating surfaces of the vibration absorbing rubber member 11 and the low-yield-strength member 12. A through hole (a') smaller in diameter than the through hole (a) is bored in a mounting part located at the lower end of a hanging column 4, each through hole (a) and the through hole (a') are aligned on the same axis, and a pin (b) equal in diameter to the through hole (a') is provided with a lock (c) and passed through the holes.