This paper describes a two-dimensional finite element integrated depth groundwater flow and contaminant transport model that was developed for an unconfined aquifer. Transient simulations for both groundwater flow and contaminant transport were performed over a 25 year period to incorporate the fluctuating pumping rates from several municipal wells screened in the contaminated aquifer. A Monte Carlo analysis of 1,000 trials was performed to assess the uncertainty of concentration breakthrough curves at municipal wells resulting from the uncertainty in contaminant transport parameters. Several model input parameters were represented by probability density functions while the hydraulic conductivity field was represented by a correlated random field. Percentiles were calculated at each time step for the 1,000 concentration breakthrough curves at each well to yield stochastic concentration breakthrough curves.