Applied mechanics is the branch of science concerned with the motion of any substance that can be experienced or perceived by humans without the help of instruments. In short, when mechanics concepts surpass being theoretical and are applied and executed, general mechanics becomes applied mechanics. It is this stark difference that makes applied mechanics an essential understanding for practical everyday life. It has numerous applications in a wide variety of fields and disciplines, including but not limited to structural engineering, astronomy, oceanography, meteorology, hydraulics, mechanical engineering, aerospace engineering, nanotechnology, structural design, earthquake engineering, fluid dynamics, planetary sciences, and other life sciences. Connecting research between numerous disciplines, applied mechanics plays an important role in both science and engineering.

Pure mechanics describes the response of bodies (solids and fluids) or systems of bodies to external behavior of a body, in either a beginning state of rest or of motion, subjected to the action of forces. Applied mechanics bridges the gap between physical theory and its application to technology.

Composed of two main categories, Applied Mechanics can be split into classical mechanics; the study of the mechanics of macroscopic solids, and fluid mechanics; the study of the mechanics of macroscopic fluids. Each branch of applied mechanics contains subcategories formed through their own subsections as well. Classical mechanics, divided into statics and dynamics, are even further subdivided, with statics' studies split into rigid bodies and rigid structures, and dynamics' studies split into kinematics and kinetics. Like classical mechanics, fluid mechanics is also divided into two sections: statics and dynamics.

Within the practical sciences, applied mechanics is useful in formulating new ideas and theories, discovering and interpreting phenomena, and developing experimental and computational tools. In the application of the natural sciences, mechanics was said to be complemented by thermodynamics, the study of heat and more generally energy, and electromechanics, the study of electricity and magnetism.

Engineering problems are generally tackled with applied mechanics through the application of theories of classical mechanics and fluid mechanics. Because applied mechanics can be applied in engineering disciplines like civil engineering, mechanical engineering, aerospace engineering, materials engineering, and biomedical engineering, it is sometimes referred to as engineering mechanics.

Science and engineering are interconnected with respect to applied mechanics, as researches in science are linked to research processes in civil, mechanical, aerospace, materials and biomedical engineering disciplines. In civil engineering, applied mechanics’ concepts can be applied to structural design and a variety of engineering sub-topics like structural, coastal, geotechnical, construction, and earthquake engineering. In mechanical engineering, it can be applied in mechatronics and robotics, design and drafting, nanotechnology, machine elements, structural analysis, friction stir welding, and acoustical engineering. In aerospace engineering, applied mechanics is used in aerodynamics, aerospace structural mechanics and propulsion, aircraft design and flight mechanics. In materials engineering, applied mechanics’ concepts are used in thermoelasticity, elasticity theory, fracture and failure mechanisms, structural design optimisation, fracture and fatigue, active materials and composites, and computational mechanics. Research in applied mechanics can be directly linked to biomedical engineering areas of interest like orthopaedics; biomechanics; human body motion analysis; soft tissue modelling of muscles, tendons, ligaments, and cartilage; biofluid mechanics; and dynamic systems, performance enhancement, and optimal control.

The first science with a theoretical foundation based in mathematics was mechanics; the underlying principles of mechanics were first delineated by Isaac Newton in his 1687 book Philosophiæ Naturalis Principia Mathematica. One of the earliest works to define applied mechanics as its own discipline was the three volume Handbuch der Mechanik written by German physicist and engineer Franz Josef Gerstner. The first seminal work on applied mechanics to be published in English was A Manual of Applied Mechanics in 1858 by English mechanical engineer William Rankine. August Föppl, a German mechanical engineer and professor, published Vorlesungen über technische Mechanik in 1898 in which he introduced calculus to the study of applied mechanics.

Applied mechanics was established as a discipline separate from classical mechanics in the early 1920s with the publication of Journal of Applied Mathematics and Mechanics, the creation of the Society of Applied Mathematics and Mechanics, and the first meeting of the International Congress of Applied Mechanics. In 1921 Austrian scientist Richard von Mises started the Journal of Applied Mathematics and Mechanics (Zeitschrift für Angewante Mathematik und Mechanik) and in 1922 with German scientist Ludwig Prandtl founded the Society of Applied Mathematics and Mechanics (Gesellschaft für Angewandte Mathematik und Mechanik). During a 1922 conference on hydrodynamics and aerodynamics in Innsbruck, Austria, Theodore von Kármán, a Hungarian engineer, and Tullio Levi-Civita, an Italian mathematician, met and decided to organize a conference on applied mechanics. In 1924 the first meeting of the International Congress of Applied Mechanics was held in Delft, the Netherlands attended by more than 200 scientist from around the world. Since this first meeting the congress has been held every four years, except during World War II; the name of the meeting was changed to International Congress of Theoretical and Applied Mechanics in 1960.