Geodynamic simulations of mantle flow repeatedly solve the Stokes equations at high memory and computational cost. We developed a Stokes solver for graphics processing units by coupling two open-source libraries. A single graphics processing unit solved the Stokes equations 6–11 times faster than a 32-core central processor, with the same accuracy. Two units further shortened the solution time of large problems. The doubled memory extended the maximum size of three-dimensional simulations.