Microbubbles in an ultrasound beam experience a primary Bjerknes force, which pushes the microbubbles against a fluid-tissue interface and deforms the tissue. This interaction has been used to measure tissue elasticity and is a common interaction in many therapeutic and diagnostic applications, but the mechanisms of deformation, and how the deformation dynamic depends on the bubble and ultrasound parameters, remain unknown. In this study, a mathematical model is proposed for the displacement of a bubble onto a fluid-tissue interface and the tissue deformation in response to the primary Bjerknes force. First, a model was derived for static loading and the model's prediction of bubble-mediated tissue displacement and stresses in tissue were explored. Second, the model was updated for dynamic loading. The results showed that the bubble is both displaced by the applied force and changes its shape. The bubble displacement changes nonlinearly with the applied force. The stress values in tissue are quite high for a distance within one radius of the bubble from the bubble surface. The model proposed here is permissible in human tissue and can be used for biomedical ultrasound applications, including material characterization.