The dissertation divides naturally into two parts. Part I is concerned with the performance of the simple shear apparatus itself and its influence on the soil properties being measured. In Part II the comprehensive behaviour of Leighton Buzzard sand (<No.14 and) No.25 BS sieves) at low stress levels 1n the simple shear apparatus is presented and discussed in detail. In a close examination of data from the Mark 6 simple shear apparatus built by Bassett (1967) and modified by Cole (1967), significant nonuniformities are shown to have developed within the samples, giving rise to large underestimates of both stress and strain quantities measured at the boundaries. The causes of this non-uniform behaviour are investigated and the major fault is found to lie in the weak contact between sand grains at the top of the sample and the upper boundary of the sample container. There follows a description of a new model of the simple-shear apparatus (Mark 7) designed by the author to overcome this and other contributary faults. Special new load cells were designed to be incorporated in the new apparatus measuring boundary stresses in the range 0.1-100 lbf/in2 (0.7-690 kN/m 2 ). In a critical assessment of the development of boundary stresses around samples tested in the new apparatus, and using X-ray methods, the local strains within those samples, it is demonstrated that conditions have been vastly improved and that the behaviour is now remarkably uniform up to the point of failure. Thus for the first time it has been possible to obtain a set of reliable and comprehensive data for Leighton Buzzard sand in the simple shear apparatus. From this data a number of simple and important patterns of behaviour have emerged. In particular it is shown that: (i) for a given initial sample density and for any stress path, provided the shear strain is monotonically increasing, the shear stresses acting on the sample are uniquely defined at any subsequent point by the stress level and by the cumulative shear strain developed from the point of first loading. (ii) the cumulative volumetric strain is similarly uniquely defined, the only exception being for test paths where the stress level decreases very rapidly with shear strain. (iii) a single two- dimensional plot of stress ratio against a voids ratio parameter derived from critical state conditions correlates the results of all tests irrespective of the initial density of the sample and of the stress path followed, provided the shear strain is monotonically increasing. Unique contours of constant shear strain appear approximately linear in this plot. Limited evidence indicates that unique contours of volumetric strain may also exist . (iv) the intermediate principal stress is proportional to the average of the remaining principal stresses for all but the very early stages of any test. In addition, an attempt has been made to separate the elastic and plastic components of strain increment. This exercise shows that: (v) for .all but the very early stages of shearing, the yield loci may be approximated to lines of constant shear strain. This provides a simple hardening law for sand in the simple shear apparatus. (vi) in plane strain stress space the yield loci are not straight lines but are significantly curved towards the axis of mean principal stress particularly at low stress levels. (vii) the state boundary line in plane strain stress space is similarly curved but is not a yield locus. (viii) the plastic strain increment ratio is a unique function of the stress state and the initial voids ratio of the sample. (ix) the power dissipated per unit volume within a sample for all but the earliest stages of shearing is proportional to the normal stress acting on the horizontat plane and to the plastic shear strain increment across it. The constant of proportionality is equal to the stress ratio at the critical state. (x) failure, defined as the onset of instability of the test system, depends on the manner of loading or unloading and only coincides with the limiting stress state envelope in tests where the normal stress on the horizontal plane is kept constant. (xi) the general conclusions of Cole (1967) with respect to the rotation of principal axes have been confirmed. During predominantly plastic deformation axes of stress and strain increment coincide while for elastic behaviour below the current yield locus, axes of principal strain increment and stress increment coincide.