In this paper,a class of new nonconforming immersed interface finite element methods are developed to solve elasticity interface problems with non-homogeneous jump conditions in two dimensions.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.Using the stabilized method,we prove the well-posedness of the discrete form.Error analysis are presented to demonstrate that such methods have an optimal convergence rate and are independent of the Lamé constants.Finally,numerical examples are presented to illustrate the theoretical results.