  Two-dimensional $O(N)$ non-linear sigma models are exactly solvable theories
and have many applications, from statistical mechanics to their use as QCD toy
models. We consider a supersymmetric extension, the non-linear sigma model on
the supersphere~$S^{N+2m-1|2m}\equiv \frac{OSP(N+2m|2m)}{OSP(N+2m-1|2m)}$. We
briefly describe its renormalization properties and lattice discretization, and
present a strategy for numerical simulations together with some preliminary
numerical results.
