During the operation of any kind of industrial power plant, the stability of the process is of primary importance since it could directly affect the safety on the performance of the system. A very important phenomenon, which affects many industrial applications, is the stability of two-phase flow in boiling channels. This phenomenon is very important in nuclear boiling water reactors since the two-phase flow, in some particular conditions, may cause flow instabilities within the reactor core subchannels. In this paper, an investigation on two-phase flow instabilities in natural circulation is carried out using the RELAP5 code and referring to a hypothetical experimental facility, at low pressure and low quality conditions. This reference experimental facility has been represented in detail in the RELAP5 code with the aim of analysing many operating conditions in which the instabilities phenomena could occur. Effects of the change in system pressure on the coolant mass flow rate have been mainly investigated in the paper, and results concerning the different operating conditions are shown. Among the analysed conditions, different two-phase flow instabilities occurrences have been identified and critically analysed, confirming the capability of the RELAP5 code to simulate this phenomenon.