Recent experimental works on high-pressure X-ray diffraction have shown that YLiF4 undergoes a reversible phase transition around 10GPa from the ambient pressure scheelite-type to a fergusonite-type structure. Different theoretical works have proposed either the M-fergusonite or M′-fergusonite as this second stable structure. Also, small changes in photoluminescence and Raman signals have been observed around 6GPa, and have not been completely explained yet. In this work we present a first-principles Density Functional Theory structural study of YLiF4. We found that the anomalies at 6GPa can be related to the structural changes observed in a scheelite to M′-fergusonite transition. We also have studied briefly different possibilities for an experimentally observed but not completly characterised third stable structure above 17GPa.