The pseudo potential method associated with the improved virtual crystal approximation is used to calculate symmetric and anti-symmetric form factors for AlP, AlAs, GaP, GaAs, InP and InAs to predict the electronic band structure of AlPxAs1-x, GaPxAs1-x and InPxAs1-x ternary alloys. The convergence of binary compounds is obtained for Ecut = 20 Hartree and 20 k- points. The fit of order 2 relating to the GGA method coincides with the VCA in AlPxAs1-x and GaPxAs1-x alloys. Elastic constants of AlPxAs1-x, GaPxAs1-x and InPxAs1-x ternary alloys for some values of phosphorus concentration are reported for the first time. AlPxAs1-x shows an indirect Г-X band gap, while GaPxAs1-x and InPxAs1-x have a direct Г- Г band gap. The band gap increases in the sequences InPxAs1-x→ GaPxAs1-x→ AlPxAs1-x. The band gap of AlPxAs1-x and GaPxAs1-x alloys in the range 1.42 eV to 3.54 eV makes them as promising material for the use in semiconductor lasers that operate in the ultraviolet spectral region. The calculated lattice constant, direct and indirect band gaps for studied materials showed great parallelism with the previously available theoretical and experimental studies.