In a wide spectrum of geotechnical applications, materials undergo large deformations and/ or large displacements. On modeling these problems with a Lagrangian finite element method, the mesh can become too distorted and re-meshing is essential. In the past decades, considerable efforts have been made to adopt what is called meshfree methods to mitigate the problems related to mesh distortion. One of these methods is the Material Point Method (MPM) that represents the continuum field as Lagrangian material points (particles), which can move through the fixed background of an Eulerian mesh. In this paper, the tensile membrane is modeled using the coupled FEM-MPM approach which adopts two-dimensional triangular elements for the membrane discretisation which is free to move through a three-dimensional mesh of non-structured tetrahedral elements. Apart from the membrane, the soil is treated with the classical procedure of MPM. To show the potential of the method and the presented membrane scheme, a failure of an embankment with and without geotextile has been presented in this paper. The analyses of failure mechanism and the embankment stability using undrained conditions were investigated to determine the critical embankment height and the corresponding geotextile forces. For the sake of comparison, Plaxis 2D with large deformation formulation is considered as a reference solution.