This paper presents the results of an extensive laboratory set of tests aimed to study the failure of the downstream shoulder of highly permeable rockfill subjected to overflow. The experimental research comprised testing 114 physical models by varying the following elements: (i) the median size of the uniform gravels (7 to 45 mm); (ii) the configuration of the dam, i.e., upstream and downstream shoulders and crest or just the downstream shoulder; (iii) the dam height (from 0.2 to 1 m), (iv) the crest length (from 0.4 to 2.5 m), (v) the downstream slope (from 1 to 3.5 H:V), (vi) the type of impervious element (i.e., central core, upstream face, and no impervious element). The tests allowed us to identify two failure mechanisms, slumping and particle dragging. In addition, the downstream slope was observed to be one of the most important variables in this parametric study, as it influenced the pore water pressures inside the dam, the failure discharge, and the occurrence of one or the other mechanism of failure.