The oscillation of a gas-filled bubble in a fluid has been studied by several approaches. In general, the fluid is considered incompressible and the gas is assumed to behave as a linear spring. Surface tension and gravity effects are usually ignored. Radiation losses of such bubbles are often determined experimentally. The present study includes surface tension effects, the gas considered is a perfect gas and the fluid an inviscid, either compressible or incompressible fluid. Free oscillations of the bubble are studied. In order to induce free motion, the gas-fluid interface of the bubble is considered to be initially at rest and then a pulse of pressure is delivered to the interior of the bubble. The ensuing motions are analyzed by a numerical integration scheme. A harmonic analysis of the pressure field is carried out after the motion of a numerical example is accomplished.