We introduce a structure-aware parallelisation technique for context-bounded analysis of concurrent programs. The key intuition consists in decomposing the set of concurrent traces into symbolic subsets that are separately explored by multiple instances of the same decision procedure running in parallel. Since the decision procedures do not cooperate but rather work on different partitions of the search space assigned upfront, the approach is naturally suited to distribution. We experiment with our technique on a selection of multi-threaded C programs known for being particularly hard to analyse. The experimental results show significant analysis speedups and excellent scalability, especially on the most complex programs and for large bounds. Our approach significantly outperforms parallel state-of-the-art solvers.