Nowadays, bladed disk rotors have many applications, and they are noteworthy wherever turbines, compressors, aircraft engines, fans, etc. are in service. Critical speeds for a rotor are rotor spin speeds in which amplitude of system may approach to infinity unless enough damping is provided. When one or more critical speeds are to be traversed, analyses are done that generally include computations to ensure that the machine is not inadvertently designed to run continuously at or near a critical speed. Typically, the cyclic symmetry assumption is used to analyze the bladed disks, but when the blades possess a slight dissimilarity in physical or structural properties, this assumption is not correct and the system dynamics undergoes a dramatic change. In this case, the bladed disk is said to be mistuned. This research has been designed to determine the critical speeds of a bladed disk rotor system with tuned and mistuned blade arrays. In order to do this, first, with the aid of a distributed-parameter model, partial differential equations of motion were derived. Two cases of modeling are considered, one assuming the longitudinal-transverse motion of the blades and the other one only assuming transverse motion. After the discretization of the equations, proper transformations were applied to the matrices of the system to obtain time-invariant matrices for both tuned and mistuned cases. For the tuned case, Coleman transformation is applied which transforms the coordinates to fixed frame coordinates called multi-blade and results in time-invariant matrices, but for the mistuned case even in spite of the use of Coleman transformation, the matrices remain time-dependent. Thus further transformations are needed that are complex transformation, permutation and modulation. By means of these matrices, modal analysis was performed on the bladed disk rotor to obtain the Campbell diagrams. It was found that taking the longitudinal vibrations of the blades into account can drastically improve the evaluation of the rotor time response as well as computing the natural frequencies of the system. An analysis on the forced vibration response was also performed through obtaining the frequency response function for the disk center. The results were compared for the tuned and mistuned system cases whereas it was seen that there are more peaks in the frequency response function of mistuned system. It shows higher probability of resonance because of mistuning, which was previously reported in earlier researches. By comparing the natural frequencies of tuned and mistuned systems, additional frequencies were found due to the presence detuning which were also seen previously. After obtaining the Campbell diagrams, a probabilistic analysis was done on the natural frequencies and it became clear that the probability density function for them may be considered as Gaussian with a good level of approximation and hence only two first statistical moments are adequate to describe the statistical properties. Keywords Rotordynamics, Bladed disk, Critical speed, Mistuning, Campbell diagram, Monte Carlo method