This thesis presents a load flow analysis for the distribution system considering uncertainties. Distribution system operation is affected by different uncertainties, such as the behavioral patterns of customers and transformer outages are the main one that disturbs the operation of distribution networks. The Monte Carlo Approach (MCA) is used to extend the forward/backward method to consider the uncertainty. Whenever there are a high load variation and transformer outage the nominal load flow analysis doesn’t show the worst case bus information. A worst-case system profile is needed in order to perform a compensation action. In this thesis a probabilistic load flow mechanism for distribution system is proposed and tested on the Bahir Dar 63 bus distribution system. The case study distribution system is analyzed for different load changes and transformer outages based on the base case results, so the worst case voltage profile is presented along the bus voltage angles using MATLAB. As load variation increases in step, the gap between the lower and upper voltage profiles becomes high and further increases when outages occurred on the transformer. MCS computed the mean, standard deviation, and variance of the output variables. At distances of 11.882 and 12.178km, nodes 53 and 54 are the furthest away from the slack node. As a result of their distance and the variation of input parameters, nodes 53 and 54 had the highest voltage deviation. The system's output voltage variation was highest at node 54 for 20% input power variations, and node 53 output voltage variation was very high for 20% input power variations and the occurrence of transformer outages on nodes 52 and 54. The ranges of output voltage in case1 at 20% input power variations, distributed in between 0.884 and 1.01pu, and that of case2 at 20% input power variation and transformer outages occurred at node 52 and 54 were distributed between 0.8 and 1.15pu. All voltage values occurring in these ranges have their own probability of occurrence in both cases.