The computational challenge in dealing with membrane systems is closely connected to the lack of bending stiffness that constitutes the main feature of this category of structures. This manifests numerically in badly conditioned or singular systems requiring the use of stabilized solution procedures, in our case of a 'pseudo-dynamic' approach. The absence of the flexural stiffness makes the membrane very prone to local instabilities which manifest physically in the formation of little 'waves' in 'compressed' areas. Current work presents an efficient. sub-iteration free 'explicit', penalty material based. wrinkling simulation procedure suitable for the solution of 'static' problems. The procedure is stabilized by taking full advantage of the pseudo-dynamic Solution strategy, which allows to retain the elemental quadratic convergence properties inside the single Solution step. Results are validated by comparison with published results and by setting up 'numerical experiments' based on the solution of test cases using dense ineshes