We used data from both permanent and temporary seismic networks on Iceland and Greenland to investigate the crustal thickness by partly reinterpreting earlier data (P receiver functions) and adding S receiver functions to better constrain the results. We obtained good conversions from the Moho and also crustal multiples in both Iceland and Greenland. The central ice covered part of Greenland has an average crustal thickness of 40 km, typical for a craton. At the edges of Greenland the crustal thickness decreases to 30--40 km. On the east coast of Greenland, where the track of the Iceland plume is thought to have affected the lithosphere, the crustal thickness is only 24--26 km. In contrast to previous studies, we find that the crustal thickness in the east and the northwest coastal regions of Iceland is more than 40 km, similar to beneath the active volcanic region. In the southwest region of Iceland and along the mid-ocean ridge, the crustal thickness is only 25 km or less. Also in contrast to earlier receiver function interpretations, which deduced a broad crust-mantle transition zone for Iceland, we find indications for a normal, sharper Moho beneath a number of sites.