The effects of efflux velocity, operational conditions, stack geometry, and buoyancy on the exhaust dispersion for a generic frigate are investigated numerically. The conservation of energy, momentum, mass, species, and turbulence equations have been solved using the finite volume method. It is found that the exhaust smoke dispersion is affected by the efflux velocity, operational conditions, buoyancy, and turbulence, as well as the geometry of the stack. The momentum of the exhaust gases and the plume height increase as the velocity ratio increases. The results for the slow ahead operation condition show that the buoyancy effect is the strongest, and the plume height is minimum for this case. The exhaust temperatures and velocity values for the full ahead operation are found to be the highest. However, the plume height for this case is not maximum. This may be attributed to the high turbulence levels for this case. It is found that the effect of stack geometry on the exhaust smoke dispersion is not significant for the geometries considered in the study. The computations are validated with the flow visualization tests carried out in a wind tunnel. The agreement between the numerical and experimental results is found to be good.