We consider finite element approximations for positive solutions of the semilinear elliptic problemwith the functiona(·) changing sign, and with superlinear growth (p< 1). We expect solutions of this problem to be saddle-points of the associated energy functional, and therefore minimization techniques are not suitable for this case. However, since solutions may be characterized as constrained maxima for a different functional, we will give a discrete version of this approach and study the convergence of approximate solutions. We also present some numerical experiments.