Electronic structures and mechanical properties of two-dimensional B2CX (X = O, S, Se) monolayers were calculated using ab initio calculations. The monolayers of B2CO, B2CS, and B2CSe are indirect semiconductors with band gaps of 1.69 eV (2.88 eV), 1.17 eV (2.23 eV) and, 0.33 eV (1.23 eV) calculated by using the generalized gradient approximation in density functional theory (hybrid functional theory), respectively. Also, to study the mechanical elastic parameters of three nanostructures, we investigate the deformation in the harmonic elastic region. B2CO is found to have comparative mechanical performance as compared to B2CS and B2CSe. In particular, B2CO has the highest in-plane stiffness value, so the calculated in-plane stiffness for B2CO is 335 N/m, and for B2CS and B2CSe is 297 N/m, and 253 N/m, respectively. The monolayers B2CS and B2CSe exhibit the negative Poisson's ratio values, giving them promising applications as auxetic materials in nanomechanics and nanoelectronics. It is also found that the electrical properties of B2CX monolayers are modified by applying strain.