Transient pore pressure tests are used to determine fluid transmission and storage behavior of porous material. In this study we investigated the coupling between stress, strain, and pore pressure during a transient pore pressure test in which a pressure step was applied to one end of a cylindrical core and a no-flow boundary was applied to the other end while the external stress was herd constant. The following results, applicable to most transient pore pressure tests, were obtained from modeling: 1) For a positive pressure step, a small pore pressure decrease develops within the sample at early times. 2) For a positive pressure step, the axial strain decreases at early times. Subsequently, the axial strain increases as the sample expands in response to diffusion. 3) The fully-coupled poroelastic response is nearly identical to an uncoupled diffusive flow response after the early time interval has passed. 4) Strain gages can be used to better constrain the hydraulic parameters by measuring pore pressure responses along the sample length. 5) Because the sample is under a constant stress boundary, the unconstrained specific storage, S sigma, is the parameter measured in many transient pore pressure tests in the laboratory.