The object of this study lies in the determination of the seismic coefficient for the plastic design based on the transient vibrations of one story buildings. The assumed characteristics of restoring force are perfect plastic and the applied earthquake wave is Kobori's, proposed one. The basic differential equation is solved by means of Phase Plane Delta Method. The following results were indicated. 1. The seismic coefficient (K_y) is influenced by the ductility factor of plastic deformation (ξ) and the natural period of buildings (T_s). With increase of them, it decreases. When ξ is larger than 4, the seismic coefficient is approximately maintained with a constant value and is not affected by the viscous damping force. 2. The optimum value of seismic coefficient K_y/K_E (K_E=earthquake coefficient) is approximately equal to 1.0 for 2.0<ξ≪3.0, x/x_<st>≑2.6, and h=0 which indicate the ductility factor, the ratio of the plastic deformation and the corresponding static deformation of building, and the viscous damping constant.