Two-dimensional, unsteady, compressible flow fields produced by the interactions between a single vortex or a pair of vortices and a shock wave are simulated numerically. The Navier-Stokes equations are solved by a finite difference method. The sixth-order-accurate compact Padé scheme is used for spatial derivatives, together with the fourth-order-accurate Runge-Kutta scheme for time integration. The detailed mechanics of the flow fields at an early stage of the interactions and the basic nature of the near-field sound generated by the interactions are studied. The results for both a single vortex and a pair of vortices suggest that the generation and the nature of sounds are closely related to the generation of reflected shock waves. The flow field differs significantly when the pair of vortices moves in the same direction as the shock wave than when opposite to it.