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Casting and welding processes introduce defects which can grow to failure under fatigue loading. It is necessary to analyze such defects to estimate fatigue lifetimes or strength loss from uninspectable flaws. An accurate analysis should include stress gradients, singular crack stress fields, and multiple flaw interactions. It must also be easily applicable to irregularly shaped mechanical components. However, it is not feasible to mesh defects due to the tedium involved, and the need to evaluate several “what if” damage scenarios. The finite element alternating method addresses these issues conveniently and accurately. It models defects by means of analytical crack stress functions, which are superimposed on systematic uncracked finite element meshes to achieve true stress fields. Functions are available for embedded or surface elliptic flaws, and other defect shapes.