In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional J (u) = integral(partial derivative Omega) f(x)u dH(N-1) over some admissible class of loads f where u is the (unique) solution to the problem - Delta(p)u + vertical bar u vertical bar(p-2) u = 0 in Omega with vertical bar del u vertical bar(p-2)u(v) = f on partial derivative Omega.