Abstract: The point estimate method is the simplest and most efficient approach for evaluating the lower order statistical moments of responses of a stochastic structural system, and moment evaluation for the function of one variable is the basis of the point estimate method. Many point estimate algorithms have been put forward and meanwhile proved to be accurate and effective by numerical cases, but it is doubtful to apply these methods to more common cases because of being lack of a theoretical support. In order to clarify this problem, the appraisal of influence factors of typical point estimate methods for probability moments of an univariate function is carried out in detail and systematically in this work, together with the evaluation of computational performance for these algorithms. Based on a number of case studies, it can be found that: 1) the main influence factors for the precision of point estimate methods are the nonlinearity degree of a function, the probabilistic category and coefficient of the variation of a random variable, while the mean value of a variable, which influences indirectly the precision by changing the nonlinearity degree of the function, is a minor factor; 2) the point estimate method proposed by Zhou & Nowak, which consists of five computational points, is the best one among four typical methods; 3) the results of all point estimate methods are not accurate enough when the nonlinearity degree of a function is strong and the coefficient of the variation of a random variable is large.