These days the analysis of all but the simple structures is carried out with the aid of computer programs based on the finite element method (FE). The user of the FE method has to decide what kind of elements should be used, and how many of them? Where should the mesh be fine and where may it be coarse? Can the model be simplified? How accurate will the answers be, and how can they be checked? One need not understand all the mathematics of the finite element to answer these questions. However a competent user must have an understanding of the preliminary mathematics and must be able to understand how elements behave in order to choose suitable kinds, sizes and shapes of elements, and to guard against misinterpretations and unrealistically high expectations. This course is a balanced theoretical and practical introduction to the use of the FE method. The first chapter deals with matrix structural analysis, which is the ancestor of the finite element method. The second chapter deals with finite element approximation and numerical integration. The third chapter is an application of the finite element method to linear plane elasticity problems. The fourth chapter deals with the analysis of thin and thick plates, which are commonly used in civil engineering as floor slabs. All the chapters include computational work in which problems are to be solved using Matlab and specialised software, such as Multiframe and ABAQUS.