Whether a shock is formed or not in a sonoluminescing gas bubble is a fundamental problem in the sonoluminescence study. The problem is numerically studied by solving Euler equations of gasdynamics in conjunction with an approximate equation of Keller type for the motion of the bubble radius. A high‐resolution TVD upwind finite‐difference scheme is used for Euler equations and a fourth‐order Runge–Kutta method for a Keller‐type equation. The result shows that, owing to the strong nonlinearity of the bubble motion, a slight increase of the driving pressure over a critical value makes the maximum collapse speed of a bubble wall supersonic, and hence the gas behavior changes from a nearly incompressible and adiabatic flow to a compressible one including a shock wave. The relation between the critical driving pressure and other parameters (the driving frequency, the initial bubble radius, etc.) is analyzed. The maximum temperature and pressure attained in the bubble are compared with those in earlier theoretical and numerical works.