This paper reports an experimental investigation involving 29 rock cores obtained from 6 boreholes drilled to various depths, up to 67.00m, in a major construction site in the United Arab Emirates as part of a ground investigation. The tested rock materials included sandstone, mudstone and calcarenite.The rock cores were prepared and tested to determine the unconfined compressive strength and the full axial and diametric stress-strain relationship using strain gauges. The deformability measurements were carried out according to the suggested methods for rock testing ISRM [1].The secant modulus and Poisson's ratio were determined from the average slope of the axial and circumferential stress-strain curve at 50% of the ultimate compressive strength. The unconfined compressive strength of the majority of the cores was found to be in the range 0.5 to 8.7Mpa,which is traditionally associated with weak rocks. A reasonable correlation between the compressive strength, secant modulus and Ultrasonic Pulse Velocity was found. However, no relationship between the axial and diametric stiffness was revealed. The testing programme highlighted the difficulties in preparing, testing and interpreting the test results of such weak rock materials.