1. A vector processing system comprising: main storage means for storing vector instructions and vector data; a plurality of vector processing units connected to said main storage means for processing different vector elements, each of the vector processing units including: (1) a plurality of vector registers; (2) at least one vector arithmetic unit, selectively connected to receive vector data from a vector register, for processing said received vector data and for sending the result of processing to a vector register; and (3) at least one data transfer circuit for transferring data between said main storage means and said vector registers; first holding means for holding the number of all the vector elements to be processed; second holding means provided for each vector processing unit for holding the number of vector elements to be processed in each processing unit; and means for determining the numbers to be set in the second holding means on the basis of the number set in the first holding means.