This book addresses a fundamental issue in the nonlinear deformation of thin-walled shell structures of arbitrary shapes. It delves into the mechanics of deformation for such structures and explores the potential of mechanical models to study their nonlinear behavior. The text analyzes established equations while also presenting new variants of the nonlinear theory for thin shells, highlighting their advantages. These equations are formulated in a way that facilitates the use of stable numerical methods. A detailed examination is provided on calculating the geometric characteristics of surfaces for non-canonical shells, where the surface is defined by a table of numbers derived from a drawing. To tackle this challenge, smoothing splines are employed. The book also presents results from numerical studies on the nonlinear behavior of rotating shells of non-canonical shapes under distributed and localized loads. This work is intended for specialists in the design and analysis of thin-walled structures, as well as for graduate students and university scholars.