The finite element method is applied to model viscoelastic sintering as a flow-based process. Momentum and mass conservation in the creeping flow limit are solved along with the upper convected maxwell constitutive equation implemented via the DEVSS-G method to determine the coalescence rate and shape of two touching spheres of equal size. While extra stresses in the neck region of viscolelastic particles showed marked differences from those in viscous (Newtonian) particles, material flows and particle shapes were nearly identical for viscoelastic and viscous systems, indicating that deviations from viscous flow predictions observed in physical systems is due predominantly to the early contact behavior described by purely elastic particle deformations. The mechanistic picture for viscoelastic sintering suggested by this work invokes elastic-dominated behavior for early stage neck growth with a transition to viscous-dominated effects at later stages. This work also demonstrates that sintering of materials possessing any degree of history dependence cannot be adequately described from a continuum-based flow model but must also include accounting of the earliest stages of contact and neck growth.