Abstract: Based on the research of structural systems with normally distributed parameters, the formulas of frequency reliability and its sensitivity were derived when the random variables were arbitrarily distributed. The unknown probability distribution function was expanded into standard normal distribution function by the way of Edgeworth expansion in the condition that the first four moments of the parameters are known. Meanwhile, the probability distribution type of the random variable moment X was loosely restricted, which was more close to the engineering practice. The efficiency and accuracy of the proposed method were demonstrated by a practical example, which is a multi-degree-of-freedom random continuous dynamic structural systems with arbitrarily distributed parameters and independent failure mode.