In this paper, a class of new immersed interface finite element
methods (IIFEM) is developed to solve elasticity interface problems
with homogeneous and non-homogeneous jump conditions in two
dimensions. Simple non-body-fitted meshes are used. For homogeneous
jump conditions, both non-conforming and conforming basis functions
are constructed in such a way that they satisfy the natural jump
conditions. For non-homogeneous jump conditions, a pair of functions
that satisfy the same non-homogeneous jump conditions are
constructed using a level-set representation of the interface. With
such a pair of functions, the discontinuities across the interface
in the solution and flux are removed; and an equivalent elasticity
interface problem with homogeneous jump conditions is formulated.
Numerical examples are presented to demonstrate that such methods
have second order convergence.