pp-waves as exact solutions to ghost-free infinite derivative gravity

We construct exact $pp$-wave solutions of ghost-free infinite derivative gravity. These waves described in the Kerr-Schild form also solve the linearized field equations of the theory. We also find an exact gravitational shock wave with nonsingular curvature invariants and with a finite limit in the ultraviolet regime of nonlocality which is in contrast to the divergent limit in Einstein's theory.