Searches for the prompt decay of supersymmetric particles in events containing photons or taus and large transverse missing momentum, performed by the ATLAS experiment running with $pp$ collisions at $\sqrt{s} = 13$ TeV, are presented. The final states that are considered are motivated by gauge-mediated and supergravity supersymmetry breaking models with stable dark matter candidate as the lightest supersymmetric particle. The increase in the center-of-mass energy of the proton-proton collisions gives a unique opportunity to extend the sensitivity to production of supersymmetric particles at the Large Hadron Collider.