The synchronization barrier is a point in the program where the processing elements (PEs) wait until all the PEs have arrived at this point. In a reduction computation, given a commutative and associative binary operationop, one needs to reduce valuesa0,...,aN-1, stored in PEs 0,...,N-1 to a single valuea*=a0op a, op...op aN-1 and then to broadcast the resulta* to all PEs. This computation is often followed by a synchronization barrier. Routines to perform these functions are frequently required in parallel programs. Simple and efficient, workingC-language routines for the parallel barrier synchronization and reduction computations are presented. The codes are appropriate for a CREW (concurrent-read-exclusive-write) or EREW parallel random access shared memory MIMD computer. They require only shared memory read and write; no locks, semaphores etc. are needed. The running time of each of these routines isO(logN). The amount of shared memory required and the number of shared memory accesses generated are botO(N). These are the asymptotically minimum values for the three parameters. The algorithms employ the obvious computational scheme involving a binary tree. Examples of applications for these routines and results of performance testing on the Sequent Balance 21000 computer are presented.