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This book is mainly oriented at persons who have already taken or who are intending to take their engineering degree and who also possess quite certain awareness of the maths - commonly within the frames of the university curriculum. The readers are expected to have some acquaintance with such subject as as the materials strength, theory of elasticity and structural mechanics and also have some knowledge of the fundamental notions of the calculus of variations. The author tried to restrict the requirements to the math skills of the readers and that is why he has not used in this publication the basics of tensor analysis even where the tensors would be relevant. The only thing readers are believed to know about is how to sum over the repeated indices. In brief, the publication is aimed at the practicing engineers rather than mathematicians. We would like to add here the senior students of engineering and also the researchers on this field, whose day-to-day activities are somehow connected with the engineering analysis. The publication could be used both as a guidebook to the deeper study of the variational principles and applicable methods in solids mechanics and mechanics of structures, and also as a standalone manual for the engineers. The text content of the book is supplemented with almost hundred figures and twenty-eight informative data tables.