This module introduces the fundamental concepts underpining the finite element method and to demonstrate its applications in enabling the solution of some important problems in Mechanical Engineering. Some necessary background in mathematics and matrix analysis will be given before the foundations of the method are covered. Various applications to one- and two-dimensional problems in fluid flow, heat transfer and solid mechanics will be treated to reinforce the concepts. The precautions and points to note in the actual practice of FE analysis such as mesh design, modelling and verification will be covered. Some instruction in the use of a commercial Finite Element software will be given and students are expected to carry out one or more projects with it. This module should give students a good foundation before taking specialised modules in numerical simulation related to specific areas.