The analytic solutions of Boulton (1954) and Neuman (1972) for transient flow to a well in an unconfined aquifer are based on the assumption that the role of the unsaturated zone can be adequately accounted for by restricting attention to the release of water from the zone through which the water table moves. Both researchers mathematically treat this released water as a time-dependent source term. The differences between the models of Boulton and Neuman are that the former neglects vertical components of flow in the aquifer, but allows for an exponential process for the release of water as a function of time, whereas the latter assumes instantaneous release from storage, but accounts for vertical components of flow. Given this set of assumptions, we examine the applicability of these two methods using a general purpose numerical model through a process of verification extension and comparison. The issues addressed include: the role of well-bore storage in masking intermediate-time behavior, combined effects of exponential release as well as vertical flow, logic for vertical averaging of drawdowns, and the sensitivity of system response to the magnitude of specific yield. The issue of how good the assumptions of Boulton and Neuman are in the contextmore » of the general theory of unsaturated flow is addressed in part 2 of this two-part series of reports.« less