An investigation is made into issues related to the existence and uniqueness of a finite deformation that generates a right or left Cauchy-Green strain field. Among the goals of this project are the determination of compatibility conditions appropriate to a prescribed left strain field in three dimensions and a constructive proof of the known compatibility conditions for a right strain field. Furthermore, methods of solution of boundary-value problems involving large deformations of continuous media are developed that exploit the foregoing compatibility conditions.
