Electromagnetic actuators are widely used because of their reliability and low-cost production. They are characterized by compact size and simple construction, therefore they are used in many imperceptible components that accompany our daily lives. The aim of this research is to develop a specific approach to modeling electromagnetic solenoid actuator that can reduce its dimensions, and at the same time increase the magnetic force and reduce its time response. The development of solenoidal electromagnetic actuator begins with the conditions in which the actuator should work. Many references in this area deals with the construction of the actuator and determination of its operating characteristics and parameters, but without optimization of its shape. Dynamic modeling of the solenoidal electromagnetic actuator is very demanding because it involves modeling and linking nonlinear subsystems. Mechatronic system of solenoidal electromagnetic actuator consists of three main subsystems: magnetic, electrical and mechanical. The magnetic subsystem is modeled in ANSYS software package (Maxwell module) and it is coupled with electrical and mechanical subsystem in Simplorer module. Numerical transient simulation is carried out using ANSYS software package using Finite Element Method. The results of numerical transient simulation are saved to output file which is passed to MATLAB, where the shape optimization of electromagnetic actuator using genetic algorithm (GA) is performed. The developed shape optimization method of electromagnetic actuator is completely independent on application of electromagnetic actuator. The electromagnetic actuator observed in this thesis has usage in high-voltage circuit breaker where specific operation conditions exist. During its lifetime, the electromagnetic actuator built into high-voltage circuit breaker mechanism is exposed to extremely high vibrations and electromagnetic field effects during the internal electric arcing. Due to the above mentioned operating conditions, it is necessary to pay an extra attention when modeling and constructing these types of electromagnetic actuators.