Measuring transport properties of rock samples under stress is essential to understanding and predicting the migration of fluids within the Earth's crust. Mudrocks play an essential role in petroleum systems as they are often the source rock and may act as a seal due to their low permeability. With increasing production from unconventional reservoirs where the mudrock is source, reservoir and seal, there is now even greater demand to understand the permeability and storativity of mudstones and tight sandstones. When hydraulic fracture treatment is used to enhance production, flow of hydrocarbons into the fractures will be ultimately controlled by the matrix permeability. Knowledge of the fluid transport properties of mudstones is currently hindered by a scarcity of published experimental data. In this thesis, a combination of permeability and ultrasonic velocity measurements allied with image analysis is used to distinguish the primary microstructural controls on effective stress dependent permeability. Permeabilities of cylindrical samples of Whitby Mudstone and Eagle Ford Shale have been measured using the oscillating pore pressure method at confining pressures ranging between 30-95 MPa and pore pressures ranging between 1-80 MPa. The results show that samples must be pressure cycled in order to obtain a reproducible behaviour, after which the relationship between permeability and effective stress can be described by an exponential law. The permeability of the Whitby Mudstone samples ranges between 7 ×10-21 m2 and 2 ×10-19 m2 (7 nd to 188 nd) and decreases by ~1 order of magnitude across the applied effective stress range. The permeability of the Eagle Ford Shale samples is slightly higher ranging between 2 ×10-18 m2 and 42 ×10-18 m2 (2 μd to 42 μd) and decreases by half an order of magnitude across the applied effective stress range. Permeability is shown to be more sensitive to changes in pore pressure than changes in confining pressure yielding values of alpha between 1.1-2.1 for Whitby Mudstone and 1.6-4.6 for Eagle Ford Shale. Gas slippage (Klinkenberg) effects are restricted to pore pressures below 10 MPa in the Whitby Mudstone and therefore do not affect the results presented. The permeability-effective stress relationship is thus empirically described using a modified effective stress law in terms of confining pressure, pore pressure and a Klinkenberg effect. Use of a simple reservoir model demonstrates that if pressure dependent permeability is not taken into account, substantial overestimation of gas flow rate and original gas in place will be made from well tests.Changes in ultrasonic velocity and pore volume were related to the observed loss of permeability with increasing effective stress, providing further insight into the nature of the permeability-controlling pore network. Combining the petrophysical data with pore conductivity modelling and microstructural analysis shows that at low effective stresses, permeability is controlled by a network of long, thin crack-like pores associated with grain boundaries. At high effective stresses, these cracks are closed and fluid is restricted to flowing through a less permeable network of higher aspect ratio, stiffer, nm-scale pores in the clay matrix. Applying the methods developed in the present work to different mudstones with a range of compositions and textures will help to refine understanding of the variability in fluid-conducting pore networks, thereby advancing the interpretation of data from well logs and well tests used for reservoir evaluation.