Needles with asymmetric bevel tips naturally bend when they are inserted into soft tissue. In this study, we present an analytical model for the loads developed at the bevel tip during needle-tissue interaction. The model calculates the loads based on the geometry of the bevel edge and gel material properties. The modeled transverse force developed at the tip is compared to forces measured experimentally. The analytical model explains the trends observed in the experiments. In addition to macroscopic studies, we also present microscopic observations of needle-tissue interactions. These results contribute to a mechanics-based model of robotic needle steering, extending previous work on kinematic models.