A nonlinear vibration isolator with High-Static-Low-Dynamic-Stiffness (HSLDS) characteristic comprised of vertical spring and horizontal spring is presented in this paper. Response of the nonlinear vibration isolator under three different kinds of base shock excitations is considered, the dynamic motion can be approximately described by the classic Duffing equation. A transformation function and ultra-spherical polynomial approximation method are employed to determine the shock response and compared with numerical method. Then performance of the nonlinear vibration isolator under shock excitations is evaluated by three performance indicies (Maximum Absolute Displacement Ratio (MADR), Maximum Relative Displacement Ratio (MRDR) and Maximum Acceleration Ratio (MAR)), and also compared with a linear one. Results show that the analytic method suits for weak nonlinearity and the performance of the nonlinear vibration isolator under shock excitations is greatly influenced by the input shock magnitude and structural parameters
