Continued development of system analysis codes has resulted in the recovery of conservatisms originally imposed on nuclear power reactors, allowing for an increase in the capacity of the nuclear power fleet. These codes also play an instrumental role in the design and certification of new reactor systems. With the increased demand for passive natural circulation and gravity driven cooling options, these codes are met with the new challenge of simulating low pressure, low flow conditions. The objective of this work is to demonstrate the effectiveness of the widely used RELAP5/MOD3.3 code to simulate boiling, condensing and flashing flows under such conditions. Several conditions of significance were selected from a published database of two-phase flow data in a vertical annulus with inner diameter of 19.1mm and outer diameter of 38.1mm. The code calculation of pressure, temperature, void fraction, interfacial area concentration, and void weighted gas velocity along the 4.5 m test section is compared with data at five axial locations. In the 2.8 m heated section of the channel the code predictions compare favorably in general, although the error does increase at low system pressure. Beyond the heated length, code predictions of condensation and flashing show more noticeable disagreement along the 1.7m unheated section. Condensation appears to be consistently under-predicted. Flashing varies from relatively good agreement to complete failure, depending on the conditions at the exit of the heated section.