Abstract: Existing third moment normal transformation (TMNT) model formula coefficients are relatively complex and the applicability range of correlation coefficients translation formula has not been clearly defined. A simplified TMNT model is proposed by simplifying the formula coefficients and by discussing the correlation coefficients. The proposed model is applicable for independent and related random variables. The explicit applicable range of a correlation coefficients translation formula is also proposed, which can be used to determine whether the proposed model can be applied for a particular engineering problem. Combined with first order reliability method (FORM), the proposed model is adopted to reliability analysis including random variables with unknown distributions. Numerical examples show that the proposed model has enough accuracy and efficiency and can be applied to conduct the reliability analysis including random variables with unknown distributions.