Within this work, direct minimization approaches on static problems of membranes are discussed. In the first half, standard direct minimization methods are discussed. Some form-finding analyses of tension structures are also illustrated as simple direct minimization approaches. In the second half, the principle of virtual works for cables, membranes, and 3-dimensional bodies are examined and they are approximated in a common way by using Galerkin method. Finally, some examples that direct minimization approaches can solve are reported.