Under periodic wave loadings offshore structures tends to be damaged due to culmulative fatigue damages. Due to uncertancies of several main parameters, the fatigue Iife itself can be modeled as random variable, in results the reliability of fatigue failure can be systematically evaluated in terms of probability. In this study, the Ang A. H - S procedure of reliability based fatigue analysis is applied with the assumptiun that random loading is modelled with Beta distrihution. The main contribution is calculation of stress ranges as structural responses under linear random waves, then the Beta disstribution of rthe loading is established.