The existence of a bubble in the vicinity of an elastic boundary appears in many situations such as medical and mechanical systems. On the other hand, bubble collapse is considered a source of energy loss in most systems and caused a lot of damages to it. This research is the first attempt to prevent bubble collapse in the vicinity of an elastic boundary by using control algorithms. In this paper, first, the nonlinear dynamic model of bubble in the vicinity of an elastic wall is introduced and then rewritten into state-space form. The second part of this paper is devoted to the design of the sliding mode controller for the bubble system, where the ultrasonic pressure plays the role of control input and the output is the bubble radius. Our main objective is to design a stabilizing controller that is able to regulate the radius of the bubble to the desired radius. At first, traditional sliding mode controller is proposed. Despite the successful tracking error, the chattering problem of this method leads us to introduce the boundary layer sliding mode control. Although the chattering phenomenon has been attenuated, it increases the steady-state error. Finally, robust integral sliding mode control is suggested to minimize the steady-state error while the chattering problem is removed. Numerical simulations including the case of parametric uncertainty are also presented. The results of this study are of immediate interest for medical applications such as ultrasound imaging and also industrial applications such as designing long-lasting pumps and valves.