Large-scale transformer-based pre-training has recently revolutionized vision-and-language (V+L) research. Models such as LXMERT, ViLBERT and UNITER have significantly lifted the state of the art over a wide range of V+L tasks. However, the large number of parameters in such models hinders their application in practice. In parallel, work on the lottery ticket hypothesis has shown that deep neural networks contain small matching subnetworks that can achieve on par or even better performance than the dense networks when trained in isolation. In this work, we perform the first empirical study to assess whether such trainable subnetworks also exist in pre-trained V+L models. We use UNITER, one of the best-performing V+L models, as the testbed, and consolidate 7 representative V+L tasks for experiments, including visual question answering, visual commonsense reasoning, visual entailment, referring expression comprehension, image-text retrieval, GQA, and NLVR . Through comprehensive analysis, we summarize our main findings as follows. (i) It is difficult to find subnetworks (i.e., the tickets) that strictly match the performance of the full UNITER model. However, it is encouraging to confirm that we can find “relaxed” winning tickets at 50%- 70% sparsity that maintain 99% of the full accuracy. (ii) Subnetworks found by task-specific pruning transfer reasonably well to the other tasks, while those found on the pre-training tasks at 60%/70% sparsity transfer universally, matching 98%/96% of the full accuracy on average over all the tasks. (iii) Adversarial training can be further used to enhance the performance of the found lottery tickets.