Bladed disks may be used in several engineering systems such as fans, impeller pumps, turbine generators and jet engines. Ideally, these systems are tuned and all blades are identical but, in practice there always exist small, random differences among the blades. Mistuning, imperfections in cyclical symmetry of bladed disks is an inevitable and perilous occurrence due to many factors including manufacturing tolerances, variations in material properties and wear in service. Each blade on a disk is almost always slightly different to the others.It can cause some unpredictable phenomena such as dramatic difference in forced vibration response.This survey explains the fundamental techniques of mistuning in some details. The 3D finite element model of bladed disk system with twenty four blades were created in ANSYS.The model then used to calculate the free and forced frequency response of the blades for the tuned system. Next, two hundred experiments, with different young’s modulus for each blade, were selected in a specified range. For each test case calculations were performed and the maximum response was obtained. Then, by integrating neural networks (NN) and genetic algorithm (GA) the worst frequency response of the mistuned bladed disk system was calculated.The problem of finding the worst specification is formulated as an optimization problem. Based on the calculated parameters, a new model was created and the maximum response of the mistuned system was calculated. Next, the tuned and mistuned responses of bladed disk system were compared. The same procedure was repeated for the case where the length of each blade was used as the perturbation parameter. In order to investigate the effect of shroud on the frequency response, the worst response of the system with and without shroud were evaluated and compared.Subsequently, the effects of mistuning on nonlinear behavior of mistuned cyclical symmetric systems like bladed disk are investigated. A nonlinear, mistuned model based on the method of multiple scales is proposed and formulated in which nonlinearity and mistuning parameter is assumed to be smal.Next, the method of multiple scales is used for finding the forced and steady state vibration response of a nonlinear mistuned lumped model. Several mistuned system were considered and solved by the proposed technique. Numerical results demonstrate that mistuning can lead to repeating and scattering of jump phenomena during the excitation frequency whereas in tuned cyclic system it occurs simultaneously.Finally, a technique using genetic algorithms developed for predicting the worst response of mistuned bladed disk with internal damping system under harmonic excitation. The worst response of the mistuned system was formulated as an optimization problem. Key Words: Mistuned Bladed Disk, Neural Network, Genetic Algorithm, Worst Response, Nonlinear Vibrations, Multiple Scale Method