Abstract: The whole deformation curve of rock represents important mechanical behaviour in the deformation and failure of rock .The problem has been deeply studied by numerous scientists .The author intends to deal with the whole deformation curve of rock .As the first step of study .the analogous calculation has been considered with the whole deformation curve of rock under uniaxial pressure in this paper .The mathematical expressions are developed piecewise ,and the constitutive law is given .Then ,the stress state of a rock specimen is computed for loading and unloading cycles step by step under the uniaxial pressure ,using the finite element method .A satisfactory result is obtained .The author will consider the problem about the deformation and failure of rock under the different confining pressure in another related paper .