Analytical solutions for aquifer response to pumping are commonly used to infer the hydraulic properties of aquifers. This dissertation develops new analytical solutions for the analysis of pumping test data from confined and unconfined aquifer.An analytical solution for flow to a partially penetrating well of infinitesimally small radius in a compressible unconfined aquifer is developed that allows inferring its saturated and unsaturated hydraulic properties from drawdowns recorded in the saturated and/or the unsaturated zone. The effects of unsaturated zoneconstitutive parameters and thickness on drawdowns in the saturated and unsaturated zones as functions of position and time is investigated; the solution is validated against numerical simulations of drawdown in a synthetic aquifer having unsaturated properties described by the van Genuchten (1980) - Mualem (1976)constitutive model; used to analyze drawdown data from a pumping test conducted by the US Geological Survey at Cape Cod,Massachusetts; and corresponding estimates of van Genuchten - Mualem parameters are compared with laboratoryvalues obtained for similar materials in the area.Drawdowns generated by extracting water from a large diameter (e.g. water supply) well are affected by wellbore storage. An analytical solution in Laplace transformed space for drawdown in a uniformanisotropic confined aquifer caused by withdrawing water at a constant rate from a partially penetrating well with storage is developed. When the pumping well is fully penetrating the solution reduces to that of Papadopulos and Cooper (1967); to that of Hantush (1964) when the pumping well has no wellbore storage; to the solution of Theis (1935) when both conditions are fulfilled; and to that of Yang et al. (2006) when the pumping well is partially penetrating, having finite radius but lacking storage. The solutionis validated against synthetic pumping test data and used to explore graphically the effects of partial penetration, wellbore storage and anisotropy on time evolutions of drawdown in the pumping well and in observation wells.The analytical solution for unconfined aquifers is extended to the case of a finite diameter pumping well with storage. The extended analytical solution is used to investigate the effects of storage in the pumping well and delayed piezometer response on drawdowns in the saturated and unsaturated zones as functions of position and time. The solution is validated against numerical simulations of drawdown in a synthetic aquifer having unsaturated properties described by the van Genuchten (1980) - Mualem (1976) model. It is then used to analyze a seven-day pumping test conducted by University of Waterloo researchers at the Canadian Forces Base Borden in Ontario, Canada; and to compare our results with those ofMoench (2008).