A significant amount of research has focused on methods to improve the eciency of cryptographic pairings; in part this work is motivated by the wide range of applications for such primitives. Although numerous hardware accelerators for pairing evaluation have used parallelism within extension field arithmetic to improve eciency, similar techniques have not been examined in software thus far. In this paper we focus on parallelism within one pairing evaluation (intra-pairing), and parallelism between dierent pairing evaluations (inter-pairing). We identify several methods for exploiting such parallelism (extending previous results in the context of ECC) and show that it is possible to accelerate pairing evaluation by a significant factor in comparison to a naive approach.