Abstract: Most studies on bubble dynamics adopting the boundary element method (BEM) were based on the incompressible potential flow theory, and the motion and deformation of a bubble in a compressible liquid was rarely studied by using BEM. An approximate theory is developed for a nonlinear and non-spherical bubble in a compressible fluid by using the doubly asymptotic approximation method. Wave equation is approximated in the early and late stages, respectively, resulting in the so-called local and global approximation equations. Matching between these two equations provides the model for the non-spherical bubble behavior in a compressible fluid domain. The numerical model is validated against the Prospertti & Lezzi equation for spherical bubbles in weakly compressible liquids with excellent agreement being obtained for the bubble radius evolution up to the second oscillation. Both numerical result and theoretical analysis show that the maximum radius decreases as the bubble oscillates. Numerical analyses are further performed for non-spherical oscillating bubbles. Bubble evolution and jet formation are simulated. Compared with that of the incompressible model, the jet velocity in the present model is smaller. Bubble oscillation near a solid boundary is further simulated based on the present model.