During the start-up phase, for safety reasons, nuclear reactors must always be far from criticality. In this respect, it is common practice to monitor at each instant the neutron flux multiplication due to the start-up source located in the reactor core: this is achieved via in-core or ex-core detectors. The simulation of this type of problems is generally performed by means of Monte Carlo codes and constitutes a real scientific challenge. It combines the need for variance reduction methods, typical of fixed-source problems, with the need to correctly represent the fission neutron source, given by the fissile materials. The aim of this thesis is to test the potentialities of the Monte Carlo code TRIPOLI-4® (developed at CEA), and in particular of its variance reduction methods, in this domain.