This Bureau of Mines report presents the initial development of a two-dimensional method of analysis for inclusions in plates in which the deformed shape of an open hole and the separate structural behavior of inclusion and plate with hole are used to obtain the stresses and strains in the inclusion only. In this report, the solution for a circular inclusion is presented because a direct verification of the results with previous solutions was possible. The numerical results were in exact agreement with those obtained with the equations of sezawa and donnell. The equations developed are less complex than those of sezawa and more general, for a circular inclusion, than those of donnell. Stresses and strains in the inclusion are in terms of the elastic constants of the inclusion and the plate and the biaxial stress field applied far away. The elastic constants can be all different. An important conclusion from this work is that a difference in poisson's ratios between inclusion and plate may be as important as a difference in young's moduli between inclusion and plate in producing the inclusion effect. Many problems in mining and rock mechanics can be treated as inclusion problems. The understanding of inclusion behavior on a physical basis should provide the solutions to some of these problems.