In the present study, numerical simulations are conducted for the collapse of an air bubble near a tissue surface by using an improved ghost fluid method. A tissue is modeled with a gelatin that was used in the experiment by Kodama and Takayama. The bubble collapse is induced by the interaction between a bubble and an incident shock wave. A flat shock wave profile and an exponential one based on the experimemt by Kodama and Takayama are utilized, and the influence of the shock wave profile on the dynamical motion of the bubble and gelatin is investigated. It is shown that the gelatin surface is depressed by the shock waves generated from the bubble. The penetration of the bubble into the depression of the gelatin, which was demonstrated in the experiment by Kodama and Takayama, is simulated successfully. The results also show that the collapse time of a bubble is longer and the width of the depression is thinner when the shcok wave with the exponential profile interacts with the bubble.