Caissons installed by suction have been in use as foundations for offshore structures. These are short, hollow cylinders capped at one end. Long versions of these foundations are currently under consideration as alternative foundations for deepwater applications. After placement on the sea bottom, first the caisson penetrates into the soil because of the self-weight, then the water contained in the interior of the caisson is removed by pumping and penetration into the soil occurs as a result of the pressure difference between the interior and exterior sides of the cap. The process affects the pore water pressure and effective stresses in the soil, and therefore becomes a significant factor in determining the shear forces on the interior and exterior cylindrical surfaces of the caisson. In turn, the friction is critical in assessing the capacity of the foundation. The research reported herein is aimed at developing a computational procedure for the evaluation of the pull-out (tensile) capacity of suction piles. In addition, in order to arrive at a better estimation of the capacity, the simulation of the installation process and its effects are considered. The numerical model is based on a finite element formulation, in which, in order to take into account the coupling between the deformation of the solid skeleton of the soil and the motion of the pore fluid, a mixture theory is used, where the saturated soil is considered as a two-phase medium, solid phase and fluid phase, expressing the equations in terms of solid displacements, Darcy’s velocities and pore fluid pressure. To analyze the interaction between the caisson and the porous medium, a frictional contact formulation is included, the coupling equations are written in such a way that the equivalent forces due to the effective stresses are extracted easily. Finally, the nonlinear behavior on the soil is taken into account through the bonding surface plasticity model. Comparisons of the computational results with recent tests conducted at the University of Texas at Austin are described.