Although the Pacific and Nazca plates share the East Pacific Rise (EPR) as a boundary, they exhibit many differing characteristics. The Pacific plate subsides more slowly and has more seamounts than the Nazca plate. Both the seismic and magnetotelluric components of the Mantle ELectromagnetic and Tomography Experiment (MELT) found pronounced asymmetry in mantle structure across the spreading axis near 17¿S. The Pacific (west) side has lower S-wave velocities, exhibits greater shear wave splitting, and is more electrically conductive than the Nazca (east) side. These results suggest asymmetric mantle flow and melt distribution beneath the EPR. To better understand the causes for these asymmetric properties, we construct numerical models of melting and mantle flow beneath a midocean ridge migrating to the west over a fixed mantle. Although the ridge is migrating to the west, the migration has little effect on the upwelling rates, requiring a separate mechanism to create the asymmetry. Models that produce asymmetric melting with a temperature anomaly require large (>100¿C) excess temperatures and may not be consistent with the observed subsidence and crustal thickness. A possible mechanism for creating asymmetry without a temperature anomaly is across-axis asthenospheric flow, possibly driven by pressures created by upwelling beneath the Pacific Superswell to the west. Pressure-driven asthenospheric flow follows the base of the lithosphere, extending the upwelling region to the west as it follows the thinning lithosphere toward the axis, and shutting off melting as it crosses the axis and encounters an increasingly thick lithosphere to the east.