The main objective of this thesis is to develop a method to investigate stability behaviours of stiffened and unstiffened panels under the influence of in-plane compression and out-of-plane lateral pressure using appropriate simplifications. A test fixture to conduct buckling experiments with lateral pressure is also designed. Due to the deflection caused by the lateral pressure, considerable complexities will be introduced in terms of loading interactions and geometric nonlinearities, which make the analysis both theoretically difficult and computationally intensive. In addition, in aerospace structures, non-cylindrical wing and fuselage panels are potentially exposed to the combined action of in-plane compression and out-of-plane pressure, and the assessment of their stability behaviours becomes an issue of growing concern of structural engineers. To this end, the study of the buckling behaviour of stiffened panels under compression and lateral pressure is of practical importance. Step by step investigations are performed on typical structures from unstiffened isotropic plates to stiffened composite panels using both analytical and finite element approaches. First, linear based methods using equilibrium and energy equations based on classical plate theories are reviewed, and predictions indicate that these methods only validate within the range of small deformation under small pressure loading. Eigenvalue buckling analysis and explicit dynamic procedures are adopted as numerical methods for verification. Simulated results of explicit dynamic procedures in Abaqus predicted the buckling loads fairly well compared with those in literature, revealing that lateral pressure has a positive impact on the stability behaviour of rectangular isotropic plates by postponing the buckling onset. Composite panels behave similarly as isotropic plates in terms of buckling and postbuckling responses. Given a large pressure, the critical buckling load of a simply supported laminate is able to reach up to four times as that of the uniaxially compressed plate. A conceptual design of a test fixture for buckling experimental studies involving compression and lateral pressure is proposed in which pressurized airbags are adopted for generating uniform pressure load. The lateral loads are controlled by the internal pressure of airbags through a pressure gauge. Compression sensors are utilized to calibrate the pressure loads by measuring the reaction forces. A rubber filler pad is laid inside the panel's bays between stringers to eliminate the unevenness on the stiffener side of the panel. Test rigs are designed with the consideration of compatibility with classical buckling experiments to lower the cost. Dynamic explicit simulations of the test reveal that the locations of the first local buckling onsets are shifted from the skin to stiffeners with the increase of lateral pressure. Buckling strengths of the entire stiffened panels exhibit an increase with the increase of lateral pressure. However, this trend is reversed when the pressure load exceeded a certain value at which stiffeners buckle before the skin.