A finite-difference time-domain (FDTD) method is used to solve the 21 2 D problem of the response of an arbitrary source, in particular, an impulsive point source, in a two-dimensional isotropic inhomogeneous medium. Cosine and sine transforms are used to reduce the three-dimensional problem to two dimensions. The complete solution is obtained by linearly superimposing several transformed field components. This provides great savings in terms of computer storage and run time over the three-dimensional FDTD model. A criterion is given to ensure the stability of this finite difference scheme. Examples of application of this analysis to actual problems such as the subsurface interface radar are illustrated.