Sound pressure fields generated by coaxial collisions of two vortex rings with equal/unequal strengths are simulated numerically. The axisymmetric, unsteady, compressible Navier–Stokes equations are solved by a finite difference method, not only for a near field but also for a far field. 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 results show that the generation of sound is closely related to the change of direction of the vortex ring motion induced by the mutual interaction of the two vortex rings. For the case of equal strength (head-on collision), the change of direction is associated with stretching of the vortex rings. Generated sound waves consist of compression parts and rarefaction parts, and have a quadrupolar nature. For the case of unequal strengths, the two vortex rings pass through each other; the weaker vortex ring moves outside the stronger vortex ring which shows a loop motion. The number of generated waves depends on the relative strength of the two vortex rings. The sound pressure includes dipolar and octupolar components, in addition to monopolar and quadrupolar components which are observed for the case of a head-on collision.