A new finite element family which contains a lambda singularity is dev
eloped. Three elements are derived; namely three-, four- and five-node
d elements which are compatible with linear, quadratic and cubic stand
ard isoparametric finite elements, respectively. The elements are test
ed on two different examples. In the first example, an edge crack prob
lem is analysed using two different meshes and different integration o
rders. The second example is a crack perpendicular to the interface pr
oblem which is solved for different material properties and, in turn,
different singularity order lambda. The results of those examples illu
strate the efficiency of the proposed elements. Copyright (C) 1996.