Kasper de Jonge takes us through parallel processing of partitions and tables in Analysis Services:
One thing that has come up several times in the last few weeks is a misconception that you cannot process multiple partitions on the same table or tables in parallel as it would cause a lock. This could be true if you try to do the parallelism yourself. Like in SQL Server you need to think about transactions, the AS engine is a transactional system too.
So, the AS engine is definitely capable of loading data in parallel but only if you let him do the puzzling on concurrency. This means you must send processing commands to the AS engine in one transaction so the AS engine can manage the locks itself. There are other benefits of letting AS doing the work like recalculating the calculated items (tables, columns etc) once instead of multiple times which improves processing performance.
Read on for an example.