Details of the singularities of residual stress at the interface edge remain unclear. This paper presents a theoretical solution of the residual stress, and discusses paradoxical problems which are related to the logarithmic singularity, based on Goursat's stress function. It is found that logarithmic singularity occurs not only in some special cases. but also in the case in which material properties and geometrical shape are near to such special cases. This paper also shows that the residual stress cannot be described only by Dunders' parameters.