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This book is recommended for students and professors who intend to obtain knowledge about hyperelastic materials, nonlinear continuum mechanics and positional finite element method. Such special class of structures has great potential for engineering and industrial applications and for academic purposes. This is due to the fact that structural components may be highly deformable, as they are getting more and more versatile. The main purposes of this book are: to address some of the principal hyperelastic constitutive models; and to present the numerical implementation of such models in a computer code which can be used for geometrically nonlinear analysis of trusses and shells under large deformation via the finite element method. It also is presented in this book some published studies about the subjects discussed.