Animal production is one of the largest contributors to ammonia emissions. A project, “Ammonia Trapping”, was designed to recover gaseous ammonia from animal barns in Spain. Laboratory experiments were conducted to select a type of membrane most suitable for gaseous ammonia trapping. Three types of gas-permeable membranes (GPM), all made of expanded polytetrafluoroethylene (ePTFE), but with different diameter (3.0 to 8.6 mm), polymer density (0.45 to 1.09), air permeability (2 to 40 L·min−1·cm2), and porosity (5.6 to 21.8%) were evaluated for their effectiveness to recover gas phase ammonia. The ammonia evolved from a synthetic solution (NH4Cl + NaHCO3 + allylthiourea), and an acidic solution (1 N H2SO4) was used as the ammonia trapping solution. Replicated tests were performed simultaneously during a period of 7 days with a constant flow of acidic solution circulating through the lumen of the tubular membrane. The ammonia recovery yields were higher with the use of membranes of greater diameter and corresponding surface area, but they were not affected by the large differences in material density, porosity, air permeability, and wall thickness in the range evaluated. A higher fluid velocity of the acidic solution significantly increased—approximately 3 times—the mass NH3–N recovered per unit of membrane surface area and time (N-flux), from 1.7 to 5.8 mg N·cm−2·d−1. Therefore, to optimize the effectiveness of GPM system to capture gaseous ammonia, the appropriate velocity of the circulating acidic solution should be an important design consideration.