Ultra-high temperature ceramics (UHTCs) exhibit a unique combination of excellent properties that makes them promising candidates for applications in extreme environments. Various UHTCs are needed due to diverse harsh conditions that UHTCs are faced with in different applications. Due to structural similarity to ZrB2, possible high melting point and possible protective oxide scale formed in oxygen rich and water vapor environments, REAlB4 (RE: rare-earth) is suggested a good candidate for UHTCs. In the present work, temperature-dependent mechanical and thermal properties of both alpha-YAlB4 (YCrB4 type, space group Pbam) and beta-YAlB4 (ThMoB4 type, space group Cmmm) were investigated by first principles calculations in combination with quasi-harmonic approach. Due to the structural similarity between alpha-YAlB4 and beta-YAlB4, their properties are very similar to each other, which are approximately transverse isotropic with properties in (001) plane being almost the same and differing from properties out of (001) plane. The results reveal that resistance to normal strain in (001) plane (similar to 460 GPa) is higher than that along [001] direction (similar to 320 GPa) and thermal expansion in (001) plane (similar to 10 x 10(-6) K-1) is lower than that along [001] direction (similar to 17 x 10(-6) K-1), which is because the stiff boron networks are parallel to (001) plane. The average thermal expansion coefficient is around 12 x 10(-6) K-1, which is fairly high among UHTCs and compatible with metallic frameworks. The combination of high thermal expansion coefficient and protective oxidation scale forming ability suggest that REAlB4 is promising for practical applications not only as high-temperature structural ceramic but also as oxidation resistant coating for alloys.