The purpose of this paper is to predict the load-elongation relationship of parallel filament yarn not only at the yield point and at the breaking point but also in the state of whole stress-strain process. A theory and a simulation of tensile properties of the yarn were proposed by using a method of statistics and the Monte Carlo method, respectively, both based on the parameters of idealized stress-strain curve of filament fibers. A comparision between the results of theoretical calculation, simulation and experiments showed good agreement. In addition, for tensile properties of the yarn, the influence of the coefficient of variance of yield strain and stress of the fibers was studied in terms of the theory and simulation.