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Finite element analyses of two and three dimensional structures often require the use of curved isoparametric elements. The overall effectiveness of such analyses by large scale finite element computer programs is often handicapped by the costly and tedious job of verifying input data and the lack of a comprehensive graphical presentation of the output. This contract work involved mathematical research concerning various approaches to improving this pre- and post processing of finite element data utilizing interactive computer graphics. A key aspect of this work was the characterization of the existence of the inverses of isoparametric mappings, as well as the development of efficient algorithms for the numerical inversion of such mappings. (Author)