Recent developments in hardware have shown an increase in parallelism as opposed to clock rates. In order to fully exploit these new avenues of performance improvement, computationally expensive workloads have to be expressed in a way that allows for fine-grained parallelism. In this paper, we address the problem of describing RDFS entailment in such a way. Dierent from previous work on parallel RDFS reasoning, we assume a shared memory architecture. We analyze the problem of duplicates that naturally occur in RDFS reasoning and develop strategies towards its mitigation, exploiting all levels of our architecture. We implement and evaluate our approach on two real-world datasets and study its performance characteristics on dierent levels of parallelization. We conclude that RDFS entailment lends itself well to parallelization but can benefit even more from careful optimizations that take into account intricacies of modern parallel hardware.