A co-operative study of the deformation of marble is described in this series of three papers. Part I deals with the experimental deformation of jacketed cylinders of dry Yule marble, at room temperature and under a confining fluid pressure of 10,000 atmospheres. Cylinders cut parallel, normal, and at 45° to the plane of foliation were homogeneously deformed varying amounts in uniaxial compression and extension. The stress-strain curves show the mechanical anisotropy of the original marble in relation to the fabric anisotropy. Applying the analytical methods of Part II, it is found that Taylor's hypothesis of the deformation of granular aggregates when applied to gliding on planes provides an explanation of the observed mechanical anisotropy. This correlation in turn provides evidence that both twin and translation gliding occur under these experimental conditions and that their relative importance depends on the original fabric and the orientation of the applied stress. Parts II and III describe other evidence which points toward similar conclusions.