This paper discusses the identification of poroelastic constants from drained isotropic confinement and pulse test. Closed form solutions of the direct problem are obtained for a very thin specimen. The validity of these solutions for a realistic aspect ratio of the core is assessed by a comparison with a finite element model. The identification problem is solved by minimizing a least square functional using an explicit gradient and a Levenberg-Marquardt algorithm. Uniqueness of this inverse problem as well as the effect of noise on input data are fully discussed. The identification procedure is then applied to measurements performed on a deep argillaceous rock (argillite of Meuse Haute-Marne).