Predicting the flow behavior of fresh concrete is important for ensuring the quality of concrete structures. While existing studies have mainly focused on static evaluations such as slump tests, dynamic fluidization caused by vibrator oscillation and the strain-rate-dependent rheology of fresh concrete as a non-Newtonian fluid have not been well studied. This study proposes a numerical simulator for the concrete filling process that can analyze both static self-weight flow and vibrator-driven flow in a consistent manner. The Smoothed Particle Hydrodynamics (SPH) method is used because it can handle large deformations and complex free-surface flows, including separation and coalescence. In the proposed formulation, unlike conventional SPH approaches that approximate viscous effects using a simplified Laplacian with constant viscosity, the divergence of the stress tensor is directly discretized. This stress-based formulation can capture spatial changes in viscosity that occur in non-Newtonian fluids. In addition, we introduce a dynamic material model in which the yield stress decreases with vibrator oscillation, so the transition from solid-like to fluid-like behavior can be simulated smoothly. The simulation results reproduce vibrator-driven flow, which supports the qualitative validity of the proposed model. Quantitative calibration against experimental time-series data is left for future work, but this study provides a basic framework for simulating the dynamic filling process of fresh concrete.