We describe the conceptual design and first application of a new method for simultaneously measuring the fluid permeability and specific storage of a rock sample. In our laboratory tests, a constant flow rate single-stroke piston pump injects fluid into a cored rock specimen placed between two reservoirs in which fluid pressure is recorded. For this geometry we have derived a new analytic solution of the governing diffusion equation describing the one-dimensional fluid flow. This new analytic solution in the time domain consists of two parts: an asymptotic linear function of time, and a transient part which decays to zero as time increases. The model predicts that the fluid pressures of the upstream and downstream reservoirs both increase linearly with time after the initial transient vanishes. The slope of the linear pressure variation depends on the specific storage of the rock sample for a given test condition, and the differential pressure between the two reservoirs is related to the permeability. If the downstream pressure is not recorded, the permeability can be calculated from the zero intercept of the linear upstream fluid pressure variation. This calculation is quite straightforward and no tedious history curve matching is required. We applied our new method to measure fluid permeability and specific storage of Westerly granite. The measured values of the permeability are consistent with those published in the literature. The main advantages of our method are the reliability of the testing method, its economy of time, and the flexibility in adapting the system parameters to tests at different conditions.