This thesis covers some of the most advanced theories in the computer analysis of skeletal structures. Linear and nonlinear finite element formulations for skeletal structures are presented. Solution algorithms for linear and nonlinear finite element equilibrium equations are described. A general direct/iterative procedure is proposed for structural analysis. In this new direct/iterative procedure, displacements are divided into a number of groups. The total equilibrium equations are split into the same number of subsystems. These subsystems are solved directly or iteratively. These solutions are further included in a main iterative procedure. A variety of available iterative (indirect) methods in the structural analysis can be related to this general procedure. New direct/iterative procedures are proposed for the linear and nonlinear analysis of frameworks by choosing different displacement groups and corresponding approximate stiffness matrices. Using these techniques, the storage requirement for the analysis of space frames can be reduced to 1/4 for linear analysis and 1/2 for nonlinear analysis. Processor time savings can be achieved for large frameworks, especially when accelerations are used.