In this paper we evaluate slug tests in shallow, fully screened wells that completely penetrate homogeneous, anisotropic, elastic, unconfined aquifers. If the free surface is incorporated into the initial boundary value problem, the dimensionless head (HD) is a function of five parameters: dimensionless time (tD), system geometry and anisotropy (η), elastic storativity (S), specific yield (Sy), and the size of the initial perturbation relative to the initial saturated thickness (λ). If the water table is assumed to be a constant head boundary, the dependence on Sy and λ is lost. Numerical solution of the problem indicates that the dimensionless response of the well (HD versus tD) is largely a function of λ, Sy, and η the response is less sensitive to S. Application of type curves derived for wells that are cased above a fixed-head water table and screened beneath will result in an overestimate of transmissivity. The overestimate will be minimized if λ and Sy are small.