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SUMMARYRefinement methods were applied in order to find the form of singularity in the free edge of a composite laminated plate. The application of a logarithmic stretched mesh in the past has led to problems by the creation of needle elements. Another disadvantage of this method has been the inability for selfadaptation. In this work, two mesh-refinement methods, employing rectangular elements, were applied in order to solve these problems. The first is the 'interface constraints' method, and the second is based on the use of a 'new mixed-hybrid transition element'. Although the first method is much simpler and almost no changes are needed in existing programs, it has a severe problem in that there is a shortage of degrees of freedom within the singularity zone. In our case this caused a totally incorrect solution. The second method needed a conceptual change in both program and analysis, but it gave accurate results.