In this work, modeling, of the complete rotor system including elastic shaft with distributed mass, rigid disks and effects of oil film in bearings and also flexibility of suspension are considered. A variety of innovations including modeling a complete rotor system with damping effects, solving vibration equations with damping terms, considering nonlinear effects and ultimately solving nonlinear equations are presented. This paper is a relatively complete work in modeling and vibration analysis of rotor considering gyroscopic effect, damping, dependency of stiffness and damping coefficients on frequency, non-linearity and solving vibration equations including these parameters. A MATLAB computer program is written based on the linear theory using finite element method. In this method four element types including shaft, disk, bearing and suspension are defined. The responses of system are obtained based on the linear theory and then, the program applies nonlinear effects and analyzes them. Finally linear and nonlinear responses of the system are compared with each other and also with the results of other papers.