This paper presents a global optimization method for continuous design variables. We call this method a generalized random tunneling algorithm (GRTA) because this method can treat the behavior constraints as well as the side constraints without using penalty parameters for the behavior constraints. The GRTA consists of three phases, that is, the minimization phase, the tunneling phase, and the constraint phase. In the minimization phase, local search technique, which is based on the gradient of the objective and constraint functions, is used. The objective of the tunneling phase is to find a point that improves the objective function obtained in the minimization phase. In the constraint phase, the feasibility of the point obtained in the tunneling phase is checked. By iterating these three phases, global or quasi-optimum may be obtained. Through mathematical and structural optimization problems, the validity and efficiency of the GRTA are examined.