The complete analysis of problems of solid mechanics must include the nonlinear effects of large deformations, inelastic material behaviour and changing boundary conditions. The finite element analysis of such problems using continuum finite elements is well established. However, the analysis of such problems using structural finite elements such as beams, plates and shells is still subject to restrictions which do not apply to continuum elements. The removal of these restrictions is important because (i) structural finite elements are widely used in current engineering practice (ii) the reduced number of variables associated with these elements leads to greater computational efficiency. The work carried out and reported in this thesis addresses the following areas of finite element analysis; the geometrically nonlinear analysis of two- and three-dimensional beams subject to arbitrarily large displacements and rotations; the elasto-plastic analysis of two- and three-dimensional beams using both multi-fibre and stress resultant approaches; the nonlinear analysis of two-dimensional reinforced concrete beams; the elasto-plastic analysis of shells using both the multi-layer and stress resultant approaches. A wide range of two- and three-dimensional problems have been analysed and the results reported. These problems cover a large number of two-dimensional beam, frame and arch problems including geometric and material nonlinearity. Results are compared with simple beam theory, other analytical solutions such as elliptic integrals, other finite element results and experimentation. Other problems analysed are three-dimensional beams with geometric and material nonlinearity, imperfect steel plates subject to large deformation elasto-plastic behaviour and two sample shell problems of practical application.