This paper presents the process of assessing the reliability of the distribution system using Non-sequential Monte Carlo simulation (NSMCS) based on random variables with multinomial distribution. NSMCS is the technique which can be easily applied for practical use to analyze the effects of uncertainty in system operations. To identify the level of system reliability, common indices based on the number of customers in areas of interest, such as SAIFI and SAIDI, are used for comparison. In this paper, the IEEE RBTS Bus-2 is used for demonstration of two case studies to verify the effectiveness of the proposed method. From the simulation results, reliability indices obtained from the proposed method are slightly different from those of base case. Including the impact of the uncertainty in operations results in reduction of system reliability.