Numerical simulation of large displacement problems in geomechanics has attracted the interest of many researchers over the past decades. In many circumstances these problems can be treated as two dimensional: plane stress or axisymmetric. However, some problems -such as the penetration of a square foundation or the DMT- do not enjoy any of these conditions. This contribution presents the extension to three dimensions of a numerical code for the simulation of large displacement fluid-saturated porous media at large strains. The proposal relies, on one hand, on the Particle Finite Element Method, known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well established in current geotechnical analyses. The performance of the method is assessed in several benchmark examples, ranging from the insertion of a rigid square footing to a rough ball penetrometer.