When nuclei of strain approach the interface of two materials, the dis
placement fields may not be unique and may depend on the direction fro
m which the interface is approached. For example, the displacement fie
lds of a center of dilatation at the interface of two materials are no
t unique and depend on the direction of approach to the interface. To
avoid misunderstanding, it can be stressed that each of the two fields
is continuous at the interface. In this paper, we show that there are
12 independent displacement functions of second-order singularities u
niquely defined at an interface. The limits of all other nuclei of str
ain at the interface are linear combinations of these 12 independent d
isplacement functions.