Selection for drought-tolerant clones has become a major challenge in rubber breeding programs undertaken to ensure the sustainability of natural rubber production, as rubber plantations are expanding in drought-prone areas. Xylem vulnerability to cavitation is a trait related to drought-induced mortality. It can be rapidly evaluated without subjecting plant materials to drought stress, making it useful in large-scale screening for drought tolerance in the near future. We first compared the most widely used techniques for measuring vulnerability to cavitation (air pressurization and Cavitron) on this species, and the effect of sample conditions (size, age and sunlight exposure), in order to ensure reliable analysis. Secondly, ten rubber clones were compared for their xylem vulnerability to cavitation in branches and petioles, and for other traits related to drought response, including stomatal response and leaf shedding occurring during a simulated drought. We also tested the plasticity of vulnerability to cavitation on two clones grown in three locations with contrasting precipitation regimes. We found no clonal variability and a small phenotypic plasticity for xylem vulnerability to cavitation in branches. However, clonal differences in xylem vulnerability to cavitation were found in petioles, and clones also showed differences in stomatal response and in leaf shedding behavior in response to a simulated drought. Our study suggests a genetic canalization for vulnerability to cavitation in organs critical for survival, such as branches, whereas there are clonal differences for traits related to drought avoidance: vulnerability to cavitation of petioles, leaf shedding behavior and stomatal response. The insights gained in this study for screening rubber tree clones for drought tolerance is also discussed.