An analytic model is developed to study the asymmetric shape deformation of a gas filled bubble in a liquid. Representing the shape distortion of the bubble surface by a set of orthonormal spherical harmonic functions Yn^m(θ,φ) of degree n and order m, a set of coupled nonlinear ordinary differential equations are derived for the evolution of the corresponding amplitudes together with the volume (spherically symmetric) mode and any induced bubble translation. The amplitude of the shape distortion together with any induced translation is assumed small and accounted for in the evolution equations to second order only, while no restriction is placed on the size of the volume oscillations. The model accounts for both viscous damping of the liquid, thermal damping of the interior gas and compressibility effects. Applying the model to the case of a submillimeter sized bubble being forced by a single frequency, temporally variant periodic pressure field, shape distortion due to the growth and subsequent saturation of parametrically induced surface instabilities is demonstrated. As a consequence of degeneracy arising from the spherical nature of the applied forcing, for a given degree n, all of the corresponding orders m are all shown to be parametrically excited for a sufficiently large driving pressure. Initial shape mode transitions and subsequent steady state evolutions are presented. The interaction of sufficiently large axisymmetric and asymmetric shape modes of neighboring degree are confirmed to give rise to bubble translation.