In this project, was developed, and validated through computer simulations, a dynamic model for a traction elevator system that moves in a plan: the vertical translations of the elevator structure and the longitudinal of a vehicle that moves on the structure. This model was employed for the development of the speed and position control of the structure, its stability in the vertical and longitudinal plane, and the speed and position control of the vehicle. To provide the two movements, it was used DC electric motors and typical transmission elements (pulleys, cables, rack-pinion gears, among others) and the movement was monitored by accelerometers and gyroscopes installed in the vehicle. From these measurements, control laws were established to guarantee the desired characteristics for the two movements. Additionally, it was used data of a real machine, from which parameters were defined for a device scale. Beyond the tools of modeling, analysis, simulation and control of dynamic systems, the laws of similarity applied to electromechanical systems were also discussed in this work.