A model for nonlinear gas bubble pulsation in marine sediments is presented. This model is then linearized to determine the resonance frequency and the damping terms for linear radial oscillations. The linear model is then used to predict the effects that such bubble pulsations will have on the sound speed and attenuation of acoustic waves propagating in gassy marine sediment. The results are compared for monodisperse populations against the predictions of a model of Anderson and Hampton and, furthermore, the additional abilities of the new model are discussed. These features include the removal of the sign ambiguities in the expressions, the straightforward implementation for acoustic propagation through polydisperse bubble populations, the capability to estimate bubble size distributions through a full acoustic inversion, and the capability to predict nonlinear effects.