Some typical rock was taken as the sample in an experiment to study the mechanical properties of white sandstone under uniaxial compression with strain rates ranging from 10^-5 s^-1 to 10^-3 s^-1. The surface displacement contours of the samples were observed and collected by using 3D-DIC system, and the difference in the deformation and failure characteristics of samples under the effect of different strain rate was also analyzed. The results show that the variation of displacement field on the surface of rock sample reflects an evolution law of failure surface, and there is a corresponding relationship between shear failure plane and concentrated displacement field. The difference in the overall axial strain mainly occurs during the period from micro-crack compaction to elastic deformation. At an initial stage of loading, there is difference in the overall radial strain. The lower end part of the sample has the largest radial displacement when the strength reaches the peak, while the upper end part is deformed under the impact of the end effect. The radial outward expansion is limited by the friction between the end face and the gasket. In addition, the local axial strain at the lower end is greater than that at the upper end. With an increase in the loading rate, rock sample has its mechanical characteristics converted from ductility to fragility. During the failure process of rock sample under the uniaxial compression with a lower loading rate, the occurred pore collapse results in friction effect due to the closure again and slippage of some cracks, thus there appears fluctuation in the stress-strain curve near the peak strength. It is shown that the mechanical parameters (peak strength, elastic modulus and Poisson's ratio) of white sandstone increase as the loading rate increases.