This paper presents experimental triaxial tests conducted on two lightly cemented sand samples on the set-up conditions of a Hollow Cylinder Torsional Apparatus (HCTA). The laboratory study has been carried out on an angular to sub-angular silica sand reinforced with Portland cement of high early strength. The samples have identical porosity/volumetric cement content ratio, η/Civ, values. The Young's modulus and shear modulus were measured by the application of a series of small unload-reload cycles at different investigation points along the triaxial stress path up to about 50% of the maximum deviatoric stress. At these investigation points, additional series of unload-reload cycles of higher amplitudes were also applied and the stiffness moduli assessed using local instrumentation. While the peak strength seems to be controlled by the density of the sand matrix, as extensive bond cementation damages occur at peak and pre-peak stages, the Young's modulus and shear modulus normalised by the void ratio function show the effect of the cementation ratio with higher values for the sample with higher cementation ratio.