This paper discusses factory and field pressure testing of tubular heat transfer equipment such as closed feedwater heaters, steam surface condensers, and power plant auxiliary heat exchangers built in accordance with Section VIII, Division 1 of the ASME Boiler and Pressure Vessel Code (the ASME Code) and repaired or altered in accordance with the National Board Inspection Code (NBIC) (The ASME issues the ASME Boiler and Pressure Vessel Code at three-year intervals and issues Addenda annually; The National Board Inspection Code (NBIC), 2007 edition (three volumes), ANSI/NBBPVI NB23-2007, The National Board of Boiler and Pressure Vessel Inspectors, Cleveland, OH). It discusses the ASME Code’s and the NBIC’s requirements for hydrostatically testing unfired pressure vessels, which include tubular heat transfer equipment. It shows by analysis that using pressure gauge indications of pressure loss to determine if there is a leak from the tube side to the shell side when the back face of the tubesheet is not visible does not reveal very small leaks or weeping. For the purposes of this paper, we define weeping, Vleak, as a leak of 20 drops/h or approximately 1 cm3/h(0.061 in.3/h). During typical half-hour hydrostatic test pressure-holding periods, such weeping would amount to 10 drops of water on the tubesheet face or 0.5 cm3(0.0305 in.3). Weeping through tube-to-tubesheet joints of high pressure feedwater heaters can lead to wire drawing (wormholing), which can materially reduce the heater life. Leaks from the channel to the shell side of steam surface condensers and auxiliary condensers can introduce brackish water into the condensate. Depending upon the fluid flowing in the tubes, contaminants can enter the shell side of other auxiliary equipment when the channel pressure is higher than that of the shell. This paper concludes that users must advise designers and manufacturers of the hazards of small leaks through the tube-to-tubesheet joints. It recommends that these three entities must agree on suitable leak tests.