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This paper presents the idea and provides an analysis of the rock breakout mechanism utilizing an undercut/breakout anchor. The new design is a modification of a standard undercut anchor, which is commonly found in applications involving steel-to-concrete anchorage. Of particular concern was the effect of the rock breakout strength on the anchor-pullout-induced failure of the rock mass. A numerical analysis was employed to model the effect of the changes to the shape and size of the breakout cones under varying rock strength conditions as a result of modifying the anchor design and loading pattern. The problem in question is pivotal for the potential evaluation of the effectiveness of the said anchor design under the non-standard conditions of its utilization.