An investigation of the supersymmetric reduction of the Wess-Zumino model is carried out for the subgroups of the Poincare group. The necessary conditions for residual supersymmetry derived from super Poincare transformations and a classification of the subalgebras of the Poincare algebra, which might give rise to supersymmetric residual systems; are obtained. Two supersymmetric reductions of the off-shell model (with interactions) by bidimensional subgroups are presented.