This project is to cover the graduation requirements for high Diploma of Higher College Of Technology. The research was on the earthquakes and it effects on the building. After that , designing system that help us to control the effect of earthquakes. This system has structure components that should be under consideration. Also, installing the Tuned Mass Dumper TMD in the structure and superstructure of building. This consisting of mass, spring and viscous dumper. The viscous dumper will absorb the energy of the vibration due to earthquakes. Part of calculations, it’s important to study the Flexibility influence coefficient. It focuses on the behavior in terms of stiffness and flexibility. Another important subject is mass stiffness and matrices. This provides the simplest representation of a building for the purposes of investigating lateral dynamic responses.