With increasing development in the oil and gas industry, exploration and production is continuously moving deeper off the continental shelf and onto the continental slopes. This increases the risk of submarine slope failures leading to damage of offshore structures. Thus there is a need to study and understand properties of offshore marine clays on slopes. This study was undertaken in order to understand better the characteristics of a sub-marine clay deposit taken from the Gulf of Mexico. This thesis presents the results of SHANSEP triaxial testing performed on undisturbed samples of Gulf of Mexico clay. Background information is given about the clay, the sampling program and the laboratory testing program. The GEOTAC Truepath automated stress path triaxial apparatus implemented for this research and the laboratory procedures used are described in detail. Data is summarized from the various types of tests run on the clay (CKoU compression and extension, CIU compression and extension tests, consolidations tests) and the stress history of the deposit is evaluated. The SHANSEP reconsolidation technique was used for a comprehensive program of Koconsolidated-undrained (CKoU) triaxial compression and extension tests at overconsolidation ratios (OCR) ranging from one to eight. Eighteen tests were run on jumbo piston core samples from one particular core. The consolidation phase of these SHANSEP tests provided most of the preconsolidation pressure values used to establish the stress history at the two test sites. These tests were used to estimate the in situ Ko and how it varies with OCR. The undrained shear phase of the tests provides detailed information on the values of S and m for use in the SHANSEP undrained strength equation, Su= 0vo = S(OCR)m, effective stress failure envelopes, etc.