The paper considers moving locally predefined (MLP) finite element remeshing technique for deep penetration of the rigid cone into homogeneous and porous medium. Remeshing presents a computational tool implemented in the form of postprocessor type software compatible with standard FEM codes. It involves a transfer operation combining both the moving least square method based on stress patch recovery and the interpolation method for transfer of state variables. The developed MLP remeshing is able to overcome numerical difficulties occurring due to large distortions of the Lagrangian mesh and contact sliding and capture steady‐state behavior. It shows good performance in modeling of cone penetration into elasto‐plastic homogeneous and porous media reaching several diameters of the cone.