The high-resolution seismic imaging of subducted oceanic slabs has become a powerful tool for reconstructing palaeogeography. The images can now be interpreted quantitatively by comparison with models of the general circulation of the Earth's mantle. Here we use a three-dimensional spherical computer model of mantle convection to show that seismic images of the subducted Farallon plate provide strong evidence for a Mesozoic period of low-angle subduction under North America. Such a period of low-angle subduction has been invoked independently to explain Rocky Mountain uplift far inland from the plate boundary during the Laramide orogeny. The computer simulations also allow us to locate the largely unknown Kula-Farallon spreading plate boundary, the location of which is important for inferring the trajectories of 'suspect' terrain across the Pacific basin.