In treatment planning of brachytherapy, absorbed dose is calculated by superposing predetermined distributions of absorbed dose to water in water for the single source according to the irradiation pattern [i.e., placement of the source(s) or dwelling position(s)]. Single-source reference water data are derived from Monte Carlo (MC) simulations and/or experiments. For reasons of positional accuracy, experimental brachytherapy dosimetry is most often performed in plastic phantoms. This work investigates the water equivalence of phantoms made from polystyrene, PMMA, and solid water for 192Ir dosimetry. The EGSnrc MC code is used to simulate radial absorbed dose distributions in cylindrical phantoms of dimensions ranging in size from diameter and height of 20 cm to diameter and height of 40 cm. Water equivalence prevails if the absorbed dose to water in the plastic phantom is the same as the absorbed dose to water in a water phantom at equal distances from the source. It is shown that water equivalence at a specified distance from the source depends not only on the size of the plastic phantom but also on the size of the water phantom used for comparison. Compared to equally sized water phantoms, phantoms of polystyrene are less water equivalent than phantoms of PMMA and solid water but compared to larger water phantoms they are the most water equivalent. Although phantom dimension is the most important single factor influencing the dose distributions around 192Ir sources, the effect of material properties is non-negligible and becomes increasingly important as phantom dimensions increase. The importance of knowing the size of the water phantom whose data underlies treatment planning systems, when using such data as a reference in, e.g., detector evaluation studies, is discussed. To achieve the highest possible accuracy in experimental dosimetry, phantom-specific correction factors should be used.