The paper presents total-stress numerical analyses of large-displacement soil-structure interaction problems in geomechanics using the Particle Finite Element Method (PFEM). This method is characterized by frequent remeshing and the use of low order finite elements to evaluate the solution. Several important features of the method are: (i) a mixed formulation (displacement-mean pressure) stabilized numerically to alleviate the volumetric locking effects that are characteristic of low order elements when the medium is incompressible, (ii) a penalty method to prescribe the contact constraints between a rigid body and a deformable media combined with an implicit scheme to solve the tangential contact constraint, (iii) an explicit algorithm with adaptive substepping and correction of the yield surface drift to integrate the finite-strain multiplicative elasto-plastic constitutive relationship, and (iv) the mapping schemes to transfer information between successive discretizations. The performance of the method is demonstrated by several numerical examples, of increasing complexity, ranging from the insertion of a rigid strip footing to a rough cone penetration test. It is shown that the proposed method requires fewer computational resources than other numerical approaches addressing the same type of problems.