Removal of the effects of the free surface from seismic reflection data is an essential preprocessing step before prestack migration. The problem can be formulated by means of Rayleigh's reciprocity theorem which leads to an integral equation of the second kind for the desired pressure field that does not include these free-surface effects. This integral equation can be solved numerically, both in the spatial domain and in the double Radon domain. Two methods are proposed to solve the integral equation: direct matrix inversion and a recursive subtraction of the free-surface multiples using a Neumann series.