The solution of two-dimensional linear elastostatic problems in the ne
ighborhood of singular points is discussed. A reliable and efficient m
ethod for computing the eigenpairs that characterize the exact solutio
n and their coefficients, called the generalized stress intensity fact
ors, by the finite element method is demonstrated. Examples, represent
ing three very different kinds of singular points demonstrate that the
method works well and produces results of high accuracy. Importantly,
the method is applicable to anisotropic materials, multi-material int
erfaces, and cases where the singularities are characterized by comple
x eigenpairs.