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The migration of the species of chromium and ammonium in groundwater and their effective remediation depend on the various hydro-geological characteristics of the system. The computational modeling of the reactive transport problems is one of the most preferred tools for field engineers in groundwater studies to make decision in pollution abatement. The analytical models are less modular in nature with low computational demand where the modification is difficult during the formulation of different reactive systems. Numerical models provide more detailed information with high computational demand. Coupling of linear partial differential Equations (PDE) for the transport step with a non-linear system of ordinary differential equations (ODE) for the reactive step is the usual mode of solving a kinetically controlled reactive transport equation. This assumption is not appropriate for a system with low concentration of species such as chromium. Such reaction systems can be simulated using a stochastic algorithm. In this paper, a finite difference scheme coupled with a stochastic algorithm for the simulation of the transport of ammonium and chromium in subsurface media has been detailed.