A theoretical analysis is presented that compares the response characteristics of the constant head and constant flowrate laboratory techniques when testing geomaterials having K<10^-10m/s. Rigorous solutions are developed for each method that describe the transient distributions of hydraulic head and hydraulic gradient within a test specimen. Expressions simulating the inflow and outflow rates across the specimen boundaries during a constant-head permeability test are also presented. These solutions illustrate the advantages and disadvantages of each method, including insights into measurement accuracy and the validity of using Darcy's law under certain conditions. The efficiency of the flow pump technique with the rigorous solution are supported by its application to a bentonite-sand mixture.