Groundwater plays a significant role worldwide in meeting water demand for domestic, agricultural and industrial uses. However, the availability of groundwater depends upon controlling exploitation and recharge of groundwater, climatic characteristics, aquifer system and the vulnerability of groundwater systems to polluting sources. In recent years, public attention has tremendously increased on groundwater contamination by hazardous industrial wastes, leachate from landfills, spills of oil and other toxic liquids, and agricultural chemicals. This necessitates improved contaminant transport models to understand the migration of contaminants characterized with nonlinear chemical kinetics. The main objective of this paper is to present a finite difference numerical model incorporating nonlinear constitutive elationships for the kinetics of decay and sorption isotherms for modeling transport of contaminants emanating from instantaneous spills in groundwater systems. The governing partial differential equation with specified initial and boundary conditions is solved using an implicit finite difference method and a computer code is developed for predicting contaminant transport behavior in groundwater system. The implicit method used here is unconditionally stable. In addition to the nonlinear decay, two nonlinear sorption isotherms described as Freundlich and Langmuir isotherms are considered in the study. Results obtained from numerical model are compared with that obtained from analytical models for the instantaneous spill. Results reveal that the predictions obtained from numerical model are found to be in excellent agreement with analytical solutions for a wide range of field conditions with regard to dispersion and source definition. Sensitivity analysis is also carried out for the quantitative description of the effect of nonlinearity in the sorption parameters and in turn on the time-space distribution of the contaminant. Such model would be helpful to water resources planners to compare alternative actions for the appropriate management of groundwater in terms of both quality and quantity.