In this study, the concrete cone capacity, concrete cone angle, and load–displacement response of cast-in headed anchors in geopolymer concrete are explored using numerical analyses. The concrete damaged plasticity (CDP) model in ABAQUS is used to simulate the behavior of concrete substrates. The tensile behavior of anchors in geopolymer concrete is compared with that in normal concrete as well as that predicted by the linear fracture mechanics (LFM) and concrete capacity design (CCD) models. The results show that the capacity of the anchors in geopolymer concrete is 30%–40% lower than that in normal concrete. The results also indicate that the CCD model overestimates the capacity of the anchors in geopolymer concrete, whereas the LFM model provides a much more conservative prediction. The extent of the difference between the predictions by the numerical analysis and those of the above prediction models depends on the effective embedment depth of the anchor and the anchor head size. The influence of concrete surface cracking on the capacity of the anchor is shown to depend on the location of the crack and the effective embedment depth. The influence of the anchor head profile on the tensile capacity of the anchors is found to be insignificant.