The MYRRHA (Multi-purpose hYbrid Research Reactor for High-tech Applications) project, started at SCK·CEN since 1999, aims at the construction of a pool-type sub-critical Accelerator-Driven System (ADS) which could also operate as a critical reactor. The primary system, enclosed in the primary vessel, is filled with Lead Bismuth Eutectic (LBE) which acts as primary coolant. The power is then delivered through four heat exchangers to four secondary loops. The secondary cooling fluid is two-phase water operating at relatively low pressure (16 bar). Four aero-condensers act as heat sinks, since MYRRHA design does not foresee any electricity generation. The MYRRHA Primary Heat eXchangers (PHXs) cover a role of fundamental importance in normal operation and accidental conditions, being part of the primary and secondary cooling system and of the Decay Heat Removal (DHR) system. It is thus highly relevant to understand the PHXs behavior under all the potential working conditions. In particular, the stability of the PHXs must be guaranteed under all operating conditions. System code models play an important role in understanding and predicting the behavior of the reactor in all conditions, from steady state to operational and accidental transients, and simulating all the postulated scenarios. A solid PHX design requires a complete assessment of two-phase flow instabilities in the secondary system water tube bundle and the potential implementation of a suitable stabilizing device (orifice) to reduce the impact of the perturbations along the channel. The stability assessment should take in consideration all the possible reactor operational power levels in order to prove the stable behavior under all operational conditions. The tube bundle stability assessment has been carried out by following a similar procedure used for BWR fuel channels, through a specific RELAP5-3D model representing the PHX and able to evaluate the propagation of a density wave in the tube length. A series of suitable boundary conditions, on both primary and secondary side, and perturbation triggers have been foreseen into the model, so to discover all kind of unstable behavior and to dimension the needed orifice to guarantee the flow stability in all operating conditions. The PHX stability analysis is initially performed on the original tube bundle without the adoption of any stabilizing devices, in order to check the natural behavior of the system. The possible adoption and design of an orifice is then conducted on the basis of this preliminary study. The system response against the various types of instabilities, before the introduction of an orifice, is not completely satisfactory: a stable flow is found within certain specific system parameters ranges. After the introduction of a suitable orifice, the system behavior becomes stable under all operating conditions against all types of two-phase flow instabilities.