The simulation of viscoelastic flow past a sphere, or a sedimenting sphere, has attracted considerableinterest since being established as a benchmark problem in computational flow dynamics [23]. As a geometry exhibiting both shearing and extensional flows, the sedimenting sphere design has the potential to probe properties of viscoelastic fluids under various conditions. In particular, we explore the low Reynolds, high Weissenberg number flow regime, in which elastic forces dominate. Using OpenFOAM, an open-source computational fluid dynamics software, we are able to implement immersed boundary conditions so that we can demonstrate unsteady startup in addition to steady-state dynamics. We find that these conditions as specified are currently unstable for reasonable sphere densities under typical gravitational acceleration, and therefore opt for unrealistically high densities and reduced accelerations (see Table 1). Nonetheless, we are able to capture realistic steady-state conditions, which we compare to the Faxen wall correction. We find that our boundary conditions, described in section 2, perform better than the Faxen correction for certain geometries. In future research, we hope to stabilize our startup dynamics for reasonable sphere densities and gravitational acceleration.