Chapter 2 introduces nonlinear systems of solid mechanics. In Sect. 2.1, the fundamental characteristics of nonlinear problems are explained in contrast to linear problems, followed by four types of nonlinearities in solid mechanics: material, geometry, boundary, and force nonlinearities. Section 2.2 presents different methods of solving a nonlinear system of equations. Discussions on convergence aspects, computational costs, load increment, and force-controlled versus displacement-controlled methods are provided. In Sect. 2.3, step-by-step procedures for solving nonlinear finite element analysis are presented, including state determination, residual calculation, convergence check, linearization, and solution. Section 2.4 introduces NLFEA, a MATLAB code for solving nonlinear finite element equations. NLFEA can handle various material models, including elastic, hyperelastic, and elastoplastic materials, as well as contact and dynamics. Section 2.5 summarizes how commercial finite element analysis programs control nonlinear solution procedures. This section covers Abaqus, ANSYS, and Autodesk Nastran programs.