The mechanisms of escape of radon from the solid structure of a particle to the free pore space are examined. According to the present state of knowledge, the most important factors affecting the radon emanation coefficient are the distribution of the parent radium atoms and the internal structure of the material. In early studies of the radon emanation coefficient, it was usually assumed that the material under investigation was homogeneous in radium distribution and in internal structure. It is now known that these assumptions are often not justified for real materials. In consequence, models based on these assumptions may not be useful in explaining the emanation process. The importance of radium distribution and internal structure is explained here, and an analysis made of differences in the internal structure of various natural and man-made materials. The analysis is then developed in order to identify the effect of different models of radium atom distribution on the emanation coefficient. Four models of radium atom distribution are presented, together with mathematical approaches for developing and finding numerical solutions for equations leading to determination of the emanation coefficient for each model.