Abstract: A two-dimensional finite-difference in time-domain (FDTD) discretization is applied to simulate finite amplitude sound pulse propagation in a reflector-focusing lithotripter. The FDTD-model is verified by the comparison of wave profiles predicted by the model with measured ones in the focal region. Special interest is set on a correct and stable modeling of spheroids with rigid or pressure release surfaces representing different scatterers modifying the pulsed pressure field in the applications. The resulting curved boundaries to be represented on a Cartesian grid tend to generate short spurious numerical waves which may lead to numerical instability. A method is presented to include arbitrarily curved boundaries in a stable manner into the underlying rectangular grid. It is verified by the comparison of the analytical solution of a simple one-dimensional seattering problem with corresponding numerical results. Using the curved boundary technique different spheroidal scatterers are included into the lithotripter model. Their influences on the significant field parameters are demonstrated. Even the conditions on the surfaces which may be of interest for simulating the interactions of kidney stones or gaseous bubbles with incident pulses of the spheroids are computable.