With the increasing use of fibre-reinforced concrete, e.g., in industrial floor and tunnel construction, the associated fastening technology in this material has increasingly become the focus of scientific attention in recent years. Over 25 years ago, design and assessment guidelines for anchoring systems in reinforced concrete were established, which have since evolved into comprehensive regulatory standards. However, these standards only address plain and rebar-reinforced concrete as anchoring bases, neglecting fibre-reinforced concrete. The design of anchorage systems in fibre-reinforced concrete has not yet been standardised. Recent studies and product certifications accounting for steel fibre reinforcement are now seeing their way to publication, supported by a fair amount of scientific research studies. This paper aims to elucidate the effects of polymer fibre reinforcement in this application through a systematic investigation. Experimental studies were conducted to evaluate the system's load-bearing behaviour failing with concrete breakouts under tensile loading. By incorporating the determined material properties of polymer fibre-reinforced concrete and their mathematical interpretation, alternative model proposals are presented to assess concrete breakout resistance. The addition of polymer fibres significantly improves the load-bearing capacity and ductility of concrete under tensile loads, transforming its quasi-brittle response into a more ductile behaviour. Although the fibres had a minor impact on overall material strength, their influence on the tensile capacity of the anchors reveal a 15-20% increase in load resistance and up to a doubling of the failure displacements.