We present the ab initio study the electronic, mechanical and structural properties of BaMnF4. We duscuss the trends in the electronic and mechanical properties of BaMnF4 under pressure up to 80 GPa. BaMnF4 belongs to the family of BaMF4-type fluorides (M = Mn, Fe, Co, Ni, Mg, Zn) which share the same orthorhombic structure. The main focus of this study is to elaborate the changes brought about in the electronic and the structural properties by applied pressure. The calculated lattice parameters have been in agreement with the available experimental and theoretical value. Band gap of BaMnF4 in our calculation is about 2.0 eV, separating the empty upper-Hubbard t2g bands and occupied lower-Hubbard eg bands. The total and partial DOS corresponding to the electronic band structure are calculated. Comparative analysis of the results of these calculations shows that the band-gap energy of BaMnF4 decreases with increasing pressure and has a minima value at a critical pressure (appr. 65 GPa), after which it increases again. Some fundamental physical parameters such as elastic constants, bulk modulus, Poisson’s ratio, sound velocities and Debye temperature were calculated and interpreted, too.