Elasmobranchs make a large contribution to bycatch in commercial trawl fisheries, which reduces the efficiency (and thus profitability of those fisheries), results in injury and mortality of those elasmobranchs, and can lead to unsustainable rates of catches. The development of bycatch reduction devices (BRDs) for elasmobranchs has been hindered, among other things, by a lack of knowledge of their avoidance behaviours and thus their vulnerability to capture (catchability). This lack of knowledge potentially affects assessments of the impact of fishing on those bycatch species. Here we examined underwater behaviours, using video analysis, of three species of elasmobranchs (two stingarees, i.e. Urolophus cruciatus and U. paucimaculatus, and one draughtboard shark, Cephalocyllium laticeps) in response to an approaching demersal trawl to quantify behavioural factors that affect their catchability. The morphologically similar U.cruciatus and U. paucimaculatus were similarly abundant, i.e. 290 and 218 individuals, respectively, but displayed different net avoidance behaviours, with U. paucimaculatus being far more likely to enter the trawl. The greater catchability of U. paucimaculatus would falsely suggest this less common species was more abundant than U. cruciatus, which has implications for any assessments of the impacts of trawling on these two elasmobranchs. Collision with trawl gear was relatively common for both Urolophus spp., and this was shown to decrease their likelihood of capture. In contrast, only 1 of the 68 individuals of the morphologically-different C. laticeps collided with gear. These results will help inform future development of BRDs and highlight that understanding the behaviour of elasmobranchs in response to capture methods should form an integral component of assessments of the impacts of trawling on this highly affected group.