Among the class of ABO(3)-type perovskite oxides, LaMO3 (M=Ga and In) compounds are investigated in cubic (Pm-3m), tetragonal (P4mm), hexagonal (P-3m1), rhombohedral (R-3c) and orthorhombic (Pbnm) phases using generalised gradient approximation (GGA) within the density functional theory. On-site Coulomb interaction is also included in the calculations (GGA+U). After the determination of the stable phase, phase transition pressures have also been calculated. Then, their full structural, mechanical, electronic, optical and vibrational properties have been studied in stable orthorhombic (Pbnm) phase. Both compounds are non-magnetic insulators in their ground states. The energy gaps (E-g) of LaGaO3 and LaInO3 compounds have been found as 3.14 and 2.55eV, respectively. The calculated elastic constants and phonon dispersion curves confirm the stability of orthorhombic phase mechanically and dynamically.