The method of self-propagating high-temperature synthesis (SHS) can be utilized to synthesize certain advanced ceramic materials, such as metal carbides, borides and silicides, directly from the elements in powder form. The method involves mixing the powders, preparing pellets from the mixture, and igniting one end of the pellet. Owing to high exothermicity of the reactions, a combustion wave can propagate through the pellet. The influence of processing conditions on propagation of the combustion wave is investigated extensively in this modeling study for pellets of finite length. It is shown that unlike infinitely long systems, the combustion wave for a finite pellet does not propagate in constant pattern. It is also shown that radiative heat losses play a major role in SHS, while convective heat losses are not relatively important.