A divide and conquer method well suited for the solution of band linear systems on massively parallel computers is presented. This method is applied in the PCG algorithm to solve large sparse linear systems. Implementations, including the low level SHMEM message passing environment and the OpenMP directives are analyzed on a T3D and an Origin 2000. Applications to the solution of Navier-Stokes equations in shallow domains are presented. Some features of the OpenMP Application Program Interface (API) useful to these applications are discussed.