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This work presents regular and singular asymptotic solutions for non-planar quasi-circular cracks. Regular asymptotic solutions, which do not give rise to hyper-singular stresses near the crack tip, are developed in the general three-dimensional setting. Singular asymptotic solutions are considered for axisymmetric problems only, because those problems do not involve hyper-singularity. The validity of asymptotic solutions for planar and non-planar cracks is investigated by comparing them with detailed numerical and analytical solutions. Also asymptotic solutions are applied to analysis of quasi-static crack growth in three dimensions.