In earthquake engineering

conventional method of seismic analysis of structure follow one of thetwo patterns: either the definitive analysis or the probability analysis. Random critical seismic responseanalysis is one of the probability analysis methods which consist of finding the critical seismic excitationfrom a class of allowable inputs that produces the highest response in a given structure. In this paper

ran-dom critical seismic analysis is used to evaluate the random critical seismic response of a SDOF water towerstructure under the Gaussian stationary random seismic excitations. Researches are carried out into the ef-fects of the paramater p

which is effectively used to control the average zero crossing rate of critical seis-mic excitation

the damp coefficient of the structure and the type and terms of the set of orthogonal func-tion on the random critical seismic response of structure. Some useful results are obtained

which can pro-vide some guidance for practical engineering.