A general time-domain approach is presented to address the acoustic transient radiation and scattering problem from fluid-loaded elastic shells. The approach is based on utilizing anin-vacuoeigenvector expansion with time-dependent coefficients for the velocity field of the shell. The time-dependent modal velocity coefficients of the shell are described by a universal set of coupled convolution integral equations. Substitution of the eigenvector expansion into the Kirchhoff integral solution leads to the external pressure field being expressed as a modal sum of convolution integrals of mode and space-dependent pressure impulse response functions with the modal velocity coefficients. Special cases which include an unbaffled finite plate and an arbitrarily shaped shell of revolution are addressed using the general approach. Simple closed-form expressions are presented for the pressure impulse response functions for the unbaffled finite plate and the on-axis response of a general shell of revolution. The characteristics of the mode and space-dependent far-field pressure impulse response functions for an unbaffled simply supported plate and a spherical shell are presented to illustrate the general characteristics of the impulse response functions.