This thesis concerns a seismic isolation mechanism for vertical component of earthquake. The vertical component of earthquake can be stronger and more destructive than the horizontal component in near-fault areas, for instance, Christchurch earthquake in New Zealand in 2011 or Bam earthquake in Iran in 2003. Therefore, this needs to be considered in designing and retrofitting structures to reduce damage to buildings and human lives. This thesis develops a numerical and experimental model of the seismic isolation based on quasi-zero-stiffness-system (QZSS) and high-static-low-dynamic-stiffness-system (HSLDSS) concepts. The results suggest the HSLDSS considered could be a practical solution for decreasing the response of the system to the vertical component of earthquake. Analytical and numerical models of a HSLDSS and a QZSS are developed. The behaviour of the mechanism subjected to static loading as well as time harmonic excitation is investigated. The harmonic balance method and the direct numerical integration method are employed to solve the equations of motion for the system. In addition, the effect of each design parameter is studied when the structure is subjected to static and harmonic excitation loadings. The impact of uncertainties in the payload as well as mistuning in the system are addressed. It is seen that the QZSS is very sensitive to any changes in payload or mistuning, while HSLDSS is unaffected by slight changes to load or initial geometry. In addition, the effects of linear and nonlinear friction elements in the model are investigated. It is seen that friction decreases the performance of the system and needs to be minimised. The response of the HSLDSS mechanism subjected to 23 near-fault earthquake ground motions is presented and discussed. Moreover, the mechanism design variables (initial geometry, static loading, stiffness of the springs) which minimise the peak acceleration, RMS response, and peak displacement are investigated. The behaviour of the linear, QZSS and HSLDSS are compared to show which case is more efficient. Although QZSS is the most effective, it is sensitive to any changes in the payload and mistuning. On the other hand, HSLDSS is less sensitive to those changes while retaining good performance and reducing the peak and RMS acceleration significantly. The experimental results are presented, the measurements taken compared to the numerical results and show good agreement. The results show significant reduction in peak and RMS acceleration for most input signals. However, for Chichi earthquake, the reverse is true. This is explained by the frequency content of the signal which has high power in the frequency range below 1 Hz. The friction force is estimated from three techniques: measurement from static tests, measurement from harmonic excitation and from the least squared error between numerical and experimental results. Among these three, the last method is found to give good agreement between numerical and experimental results for all earthquake inputs. The developed mechanism is shown to be efficient in isolating structures with one support subjected to earthquake inputs. It reduces the force transmission from the base to structures during earthquakes.