A two-dimensional finite element model was developed to predict water flow and nitrogen species transport and transformation in variably saturated soil. In the finite element analysis various numerical algorithms were examined to evaluate methods of improving the efficiency of the traditional finite element approach. Results indicate that when undeformed linear rectangular elements or linear triangular elements were used, the method of influence coefficients is more efficient than traditional numerical integration method in evaluating the element matrices while maintaining accuracy. Also with moderately nonlinear flow problems, use of a fourth order Runge-Kutte method produced improved efficiency over fixed or variable time step schemes for time integration. Hysteretic simulations with air entrapment showed that effects of hysteresis are greatly enhanced by the presence of air entrapment due to large differences in water contents between different saturation paths. Flux-controlled boundary conditions produced negligible hysteretic effects while maximum effects were caused under potential type boundary conditions. The magnitude of hysteretic effects are also affected by the definition of initial condition. Heterogeneity in the porous medium tends to reduce hysteretic effects. The finite element model developed to solve the convective-dispersive equation for nitrogen transport utilized an upstream weighting scheme to reduce numerical oscillation associated with low dispersion coefficients. The accuracy and validity of the model were evaluated using both published and field data. The results indicate overall predictions of various nitrogen fractions are quite sensitive to the first order nitrification rate. However, use of kinetic constants based on published results in the literature, especially in the absence of detailed field investigations, may still be sufficient to provide dependable results through simulations. Hysteresis greatly affects the transport of nitrogen species under potential type boundary conditions, but these effects are reduced substantially in the presence of high intensity line sources. Under such circumstances, it is sufficient to neglect hysteresis and use either the main drainage or the main wetting branch of the pressure-saturation relationship for simulations. / Ph. D.