Abstract: Tt is proved in this paper that a singularity occurs in quadratic or cubic Lagrangian isoparametric Unite elements when the side-nodes and internal nodes are displaced properly from their normal position. As the quadrilateral elements are collapsed into triangular elements around the crack tip and the side-node and internal node positions on standard la-grangian isoparametric elements are so chosen that the singularity occurs exactly at the corner of an element, it is possible to obtain inverse square root singularity of the strain field at the crack tip. In addition, a transition element can be easily constructed by shifting side-nodes and internal nodes to some properly calculated points. Stress intensity factors may be computed with considerably high accuracy by using transition element between crack-tip singular elements and remaining non-singular elements. Several numerical examples show collapsed Lagrangian isoparametric singular element gives excellent results even when a comparatively few elements and nodes are used.