Many researchers have been trying to use the implicit parallelism of logic languages parallelizing the execution of independent clauses. However this approach has the disadvantage of requiring a heavy overhead for processes scheduling and synchronizing, for data migration and for collecting the results. In this paper it is proposed a different approach, the data parallel one. The focus is on large collections of data and the core idea is to parallelize the execution of element-wise operations. The target language is SEL, a Subset Equational Language. An abstract machine for it, the SAM (Subset Abstract Machine), is outlined, which, under certain points of views, belongs to the WAM family. The data parallel structure of the SAM is here explained and some examples of how it works are given. Eventually it is explained the role of abstract analyzers in this framework and it is presented the plan for the future research.