Structural optimization has been developed by two methods. One is the direct method which applies the Nonlinear Programming (NLP) algorithm directly to the structural optimization problem. This method is known to be very excellent mathematically. However, it is very expensive for large-scale problems due to the one-dimensional line search. The other method is the approximation method which utilizes the engineering senses very well. The original problem is approximated to a simple problem and an NLP algorithm is adopted for solving the approximated problems. Practical solutions are obtained with low cost by this method. The two methods are compared through standard structural optimization problems. The Finite element method with truss and beam elements is used for the structural and sensitivity analyses. The results are analyzed based on the convergence performances, the number is function calculations, the quality of the cost functions, and etc. The applications of both methods are also discussed.