Every nuclear power plant has a control rod cluster for reactor scram upon command. I focused on a reactor shutdown without usage of the control rods in a two-loop pressurized water reactor power plant. This scenario is called an anticipated transient without scram. In the beginning of this task I explain the basics of a two-loop pressurized water reactor power plant. I explain the basics of nuclear fission, the role of the moderator, reactivity, residual heat. Then, I explain the importance of reactivity coefficients, because they play a great role in self-regulation of the reactor. There is also a chapter about the safety in nuclear power plants and about the design basis accidents connected with anticipated transient without scram. I also included a chapter about the PCTran simulator, where I explain how it works and how to use it. I made a simulation of a reactor shutdown, which is achieved with boric acid injection to the primary system. Simulation was executed in a simplified nuclear power plant simulator PCTran. Reactor was successfully shut down 580 s after beginning of injection additional boron to the primary system. After shutdown there is always residual heat present, which the simulator failed to present. I calculated residual heat generation using Patterson-Schlitz formula in Matlab and then added this calculation up with the reactor power to get better and anticipated results. Analyzing transients of different parameters I concluded that the power plant achieves safe state after the anticipated transient without scram.