Abstract: Inerters and negative stiffness devices can improve the energy dissipation performance of vibration absorbers. An increasing number of applications of them in novel high-performance vibration suppression have been witnessed. In this paper， analytical parametric optimization analyses on the tuned inerter mass systems with negative stiffness （NS-TIMS） are performed. A unified model of governing equations and transfer functions for NS-TIMS under different installation locations， application scenarios （such as inter-layer vibration absorption， and base isolation） and excitation types is established. Based on the fixed-point theory， the optimal parameters of NS-TIMS considering both H_∞ and H₂ norms are analytically derived. Considering typical application conditions， the analytical formulas are further analyzed and simplified. Consequently， the design formulas for the optimal parameters of NS-TIMS based on the “equivalent inertial mass ratio” are proposed. The application scopes of the design formula are discussed. Through numerical cases on the practical examples of wind-induced vibration control and seismic base isolation， the effectiveness of the design formulas considering the actual structural damping ratio and spectral characteristics of stochastic excitations is verified. It is also revealed that NS-TIMSs have superior performances in both high flexible structure vibration absorption and auxiliary base vibration isolation.