This work is a comparative study of the various numerical techniques used for analyzing membranes. Membrane analysis is complicated by the fact that local instabilities occur in membranes in the form of small waves or ‘wrinkles’ in zones in which compression tends to appear. This is attributed to their negligible flexural stiffness. Broadly, two approaches exist in the wrinkling analysis of membranes. They are bifurcation analysis and analysis with membrane elements augmented with wrinkling models. In the former approach we can get the wrinkle details while the latter approach gives only the wrinkling zone. The present numerical strategy falls in the category of bifurcation analysis, where we make use of an energy-momentum conserving time integration algorithm in the context of a hybrid element formulation. The solution obtained through this procedure is considered to be accurate, since there are no kinematic assumptions (plane stress, etc.) made in the formulation and we achieve convergence with respect to mesh refinement. We show in this work that the wrinkling process not only depends on the stiffness matrix but also on the transient process. To show this a pseudo-dynamic scheme which is commonly used, is implemented within the hybrid formulation and we show the differences that arise between this scheme and the present method, over some benchmark problems. In this work, we also implement a wrinkling model proposed by Roddeman and finally the advantages and disadvantages of various numerical techniques are discussed.