The manner in which stiff biological objects, such as whole bones and teeth, deform under load can provide direct insight into their in vivo functions, while highlighting the relations between their structure and materials properties. A new approach for studying the mechanical functions of such objects, using as an example the crowns of human teeth, is developed. Tooth-crown deformation under a compressive load is determined in water using laser speckle interferometry. The deformation patterns are analyzed using a novel procedure that reveals the relative magnitudes of 3D displacements of the outer surface. Nanometer-scale deformations of natural teeth were compared to deformations of identical acrylic replicas, in order to differentiate between contributions of the structure-material properties from contributions of morphology. It is shown that human premolars deform in a manner that is largely controlled by shape; in natural teeth, the enamel cap appears to displace mainly as a rigid body, undergoing moderate deformation. These observations contribute to the understanding of whole-tooth performance under load. The approach for analyzing the deformation of loaded whole objects is directly applicable to the study of many stiff biological specimens, including comparisons between normal and altered (repaired or genetically modified) bones.