On the basis of the Euler equations, the interaction of a shock wave in a combustible gas with an elliptical bubble of an inert gas of increased density is numerically simulated within a plane two-dimensional formulation. The finite-volume Godunov-type method of the second order of approximation is applied. Gas combustion is modeled using the Korobeinikov-Levin two-stage kinetics. Various values of the Mach number of the incident wave and the elongation of the inert bubble are considered, and the refraction and focusing of the incident shock are described. Qualitatively different regimes of gas detonation initiation have been found, including direct initiation by a strong wave, ignition upon reflection of an average-intensity wave from the gas interface, and upon focusing of secondary shock waves at lower shock Mach numbers. The dependence of the ignition mode on the shock intensity and the shape of the bubble is determined.