A novel massively parallel technique for rigorous simulation of topography scattering in optical lithography has been developed and tested. The method is equivalent to the time-domain finite-difference method (TDFDM) used in electromagnetic scattering simulations, but exploits the parallel nature of wave propagation and the power of recent massively parallel architectures such as the Connection Machine. A working code called TEMPEST has been implemented on a Connection Machine CM-2 having 1 to 32 K processors with up to 1 M virtual processors. Numerical accuracy comparable with that of other fully rigorous methods was achieved. A very significant finding was that the solution required constant time per iteration for problems ranging from a few thousand unknowns up to one million, provided the ratio between the problem size and the number of processors is kept constant. The suitability of TEMPEST for solving a large class of topography structures important in alignment, metrology, and lithography is illustrated by examples.>