Traditional soil penetration activities such as site investigation and pile driving are energy-intensive and typically cause significant disturbance to surrounding soils and the environment. In recent years, researchers have attempted to solve the abovementioned problems by developing self-burrowing tools and probes on the basis of biological inspiration. Animals such as razor clams are capable of efficiently burrowing into soils using a dual-anchor mechanism, which cyclically alternates penetrating the back (shell) and front (foot) anchors to achieve forward movement. Due to inherent complexities of the self-burrowing mechanism, the interaction between a clam-inspired probe and soil is not fully understood yet. This study employs models based on the discrete element method (DEM) to investigate this soil-structure interaction problem. The soil sample is filled with a scaled discrete quartz sand analogue. The self-burrowing behavior of the probe is fully modeled using force-control motion, which enables realistic interaction with the surrounding soil. The strategy of tip oscillation is also employed to reduce soil penetration resistance. The simulation results show that the self-burrowing probe can achieve significant advancement, especially when tip oscillation is used. Micromechanical observations such as contact force networks and displacement fields are also provided to better understand the interaction between the soil and the bio-inspired probe. This study provides meaningful guidance for future self-burrowing probe development.