Migration algorithms based on Fourier methods are naturally parallel. The modeling algorithm which is the conjugate transpose of the migration algorithm (or vice-versa) preserves all the parallel features of the direct (migration) algorithm. I implemented two Fourier based modeling algorithms on the Connection Machine. Both methods are the conjugate transpose of two migration algorithms (Phase Shift Plus Interpolation and Split-Step). I tested the algorithms on 3-D and 2-D variable velocity models. I compare both methods considering speed and accuracy.