In this paper, two models to establish the minimum exposure path in a randomly placed radioactive sources enclosure are developed. The first model establishes the minimum exposure rate path and the second establishes the normal, to the inlet and outlet surfaces, path that gives a minimum exposure. The path that gives the least exposure is chosen. Although the point kernel technique is utilized and the enclosure is assumed rectangular with randomly placed radioactive point sources, the two models are independent techniques and can be easily incorporated with deterministic and statistical methods as well as other types of enclosures and source geometries.