This is a textbook on models and modeling in mechanics. It introduces a new unifying approach to applied mechanics: through the concept of the open scheme, a step-by-step approach to modeling evolves. The unifying approach enables a very large scope on relatively few pages: the book treats theories of mass points and rigid bodies, continuum models of solids and fluids, as well as traditional engineering mechanics of beams, cables, pipe flow and wave propagation.Models of Mechanics complements existing books that deal with continuum mechanics. In contrast to such books it gives a setting that is broad enough to encompass also the mechanics of mass points, and theories of beams and other intrinsically one-dimensional bodies. An obtained knowledge of the unifying approach can be a base for advanced studies of fluid and solid mechanics, as well as specializations in mechatronics, control and structural optimization. The book is ideal to use in conjunction with equation-based finite element programs like FEMLAB and FlexPDE. It provides tools for organizing and structuring the broad discipline of mechanics, as well as a platform for deriving new models of applied use.