Semi-solid flow batteries (SSFBs) provide a highly scalable energy storage alternative for the reliable use of intermittent renewable energy sources. In this work, a new pseudo three-dimensional (P3D), multi-scale and multi-physics approach to the modeling of SSFBs is presented which includes the correct way to model flowing active particles. Two coupled continuum domains; one representing the battery and another representing the electrochemically active particles, are used as the computational solution strategy, to resolve the characteristic multi-scale electrochemical phenomena. In modeling the flowing particles, solid-state diffusion is applied as the single transport mechanism, contrary to previous investigations which included convection/advection. Time dependent voltage profiles, as well as spatial distributions of the state of charge in the SSFB active particles are herein examined and a Ragone plot for a SSFB is unveiled for the first time. Although presented in the case of a nickel-metal hydride SSFB, this P3D model framework is adaptable to any other SSFB chemistry, based on Li-ion or Na-ion active materials for example.