In this study, the physical such as structural, electronic, anisotropic elastic and lattice dynamic properties of YXB4 (X = Cr, Mn, Fe and Co) compounds have been investigated. The electronic properties including band structure and corresponding partial density of states for YXB4 have been calculated. YFeB4 and YCoB4 compounds are found to have metallic behavior while YCrB4 and YMnB4 have semiconductor behavior. Also, the compounds are found to be as non-magnetic materials. The calculated elastic constants indicate that these materials are mechanically stable due to satisfying Born stability criteria. In addition, the second order elastic constants and related polycrystalline elastic moduli (e.g. shear modulus, Young's modulus, Poisson's ratio, Debye temperature, sound velocities) are determined and the results are discussed in detail. The mechanical anisotropy is discussed using several anisotropy indexes and two-dimensional and three-dimensional surface constructions are obtained. All the compounds have dominantly covalent bonding and they are brittle materials. YCrB4 is found to be as a super hard material. YFeB4, YCoB4 and YMnB4 are found to be as hard materials. The dynamical stability of these compounds has been studied and it has been found that YCoB4 is dynamically unstable. In addition, the thermodynamic properties (heat capacity, free energy, etc) of these compounds have been obtained and discussed in detail.