To perform easily and highly accurately time history response analysis of an object with an attenuation constant h indicating a vibration frequency nondependent characteristic.

A causal unit imaginary function comprising an imaginary part expressed by the sum of a regular component wherein a frequency shows a value of (2n-1)-(2/m) in the range from (n-1) m to n m and a singular component showing a value of (2/m) regardless of the frequency , wherein the frequency shows a value of (2n-1) in the range from (n-1) m to n m, and a real part corresponding to a Hilbert transformation value of the regular component, or its imaginary part is transferred into a time domain, to thereby determine an impulse response value, and a rigidity reduction rate () and the attenuation constant h() in the equation (1) acquired by substituting the impulse response value: [Ms]{u"(t)}+{F(,t)}=-y0"(t)[Ms]{1} are switched to values corresponding to a strain level of the object at each time, and simultaneously operated at each t unit, to thereby perform time history response analysis of the object.