The sieving equipment is widely used to make the bulk substance is divided into two or more levels of granularity. The vibrating screen is the most common screen equipment used in the mining industry. The development and the problems of the domestic large-scale screening equipment started from the 1970s. We have done a lot of work and made great achievements in terms of the development of large-scale screening machine. For the screening machinery, the length and width of the screen surface are two important structural parameters we should carefully consider. They are the first two problems encountered in the design and selection of the screening machine. According to the screening theory, the width of the screen surface is associated with the processing capability of the screening machine. Under the same conditions, if the sieve surface is wide, the processing capacity will be great. The length of the sieve surface is associated with the screening efficiency. Under the same conditions, to appropriately lengthen the sieve surface can improve the screening efficiency. However, according to the mechanism of the probability sieving, with the lengthening of the sieve surface, the particle size whose diameter is greater than the separation particle diameter increases which makes the screening efficiency decrease. From the above analysis, we can know that the there is an optimal value for the screen surface to make the screening efficiency to be the highest. Based on the probability statistics, we can establish the model, which can better reflect the through screen probability of the particles along the long direction of the sieve, which provides certain theoretical basis for the design of the probability screen. We can deduce the formula of the through screen probability for the particles along the sieve. However, the formula is too complex. In addition, the formula does not directly point out function relationship between the efficiency and the length of the sieve. It is extremely inconvenient in the industrial application. The experts of Henan Hongxing Mining Machinery use the three-dimensional discrete element method to simulate the probability of screening process and establish the function relationship between the screening efficiency and the length of the screen surface, which is more convenient and simple.