Abstract
Let S=K[x(1), ... , x(n)] be a polynomial ring in n variables over a field K. Stanley's conjecture holds for the modules I and S/I, when I subset of S is a critical monomial ideal. We calculate the Stanley depth of S/I when I is a canonical critical monomial ideal. For non-critical monomial ideals we show the existence of a Stanley ideal with the same depth and Hilbert function.