The paper describes and examines a technique which permits the power-flow problem in a power system to be analysed probabilistically instead of using normal deterministic methods. All the nodal loads and generation are defined as random variables and the power flow in each line is computed in terms of a probability density function. The expected values and standard deviation of each power flow are also calculated, and, in addition, the overall balance of power in the system is determined in terms of a density function. The purpose of this analysis is to account for the errors and statistical variations known to exist in the operation and planning of systems within one solution. This enables the power-flow problem to be treated objectively and allows quantitative assessment of reliability and security. The paper compares the results obtained probabilistically with those that would be obtained deterministically, and shows the much wider range of information gained in this type of analysis.