This method depends on the dividing up of a body into discrete elements, which may be triangles, squares or other defined shapes, and analysing the response of the body as a whole as the sum of what the response is of each element of the body.

Each element is characterised by the value of a quantity (stress, displacement) at the nodes (corners) of the element and values at points in between were estimated by interpolation. The method was developed in the 1950s for problems in structural engineering, especially in the aeronautical industry.

The first usage of the term "finite element" came in 1960 and the generalisation of the method to solve problems in fields other than structural engineering, such as heat transfer, came in the late 1960s.

Since the calculations were numerical and elements were often small in relation to the size of components or structures, the use of the finite element method was somewhat restricted until cheap powerful computing facilities (hardware and software) became available. Initially, problems tackled by this method were one-dimensional but the developments of the method, especially with increased computing power available, has been extended to two and three dimensions.