Ti₃O₅ is a highly anticipated functional material due to its intriguing physical properties and multi-incentive phase transition process. This material undergoes a reversible first-order phase transition between λ phase and β phase, accompanied by drastic changes in the electronic and atomic structure. The amazing way of changing phase such as light, heat, pressure and electric current makes this material promise to be used in future optical information storage and heat storage. In this work, structural, elastic, electronic and optical properties of λ-Ti₃O₅ and β-Ti₃O₅ are calculated by using a first-principles approach, according to density functional theory (DFT). The LSDA, GGA-PBE, GGA-91, GGA-PS and GGA-RP are compared among them to obtain a suitable method of characterizing the crystal structure and electronic structure of λ-Ti₃O₅ and β-Ti₃O₅. The energy gap at the Fermi level of β-Ti₃O₅ can be obtained only when the extra Coulomb correlation U effect of Ti 3d electrons is considered. A complete set of elastic parameters for both phases are first reported. The calculated elastic constant satisfies the Born stability criterion, indicating that λ phase and β phase have good mechanical structural stability. The two phases are more resistant to volume changes than to shape changes and both behave as ductile materials. On the (010) plane, the elastic anisotropy of λ phase is weaker than that of β phase. Studies on the electronic structure show that the local charge of Ti₃ is transferred to Ti₂, resulting in the transformation of the semiconductor β phase to the metal λ phase. There are large differences in optical property such as absorption and reflectivity between these two structures, indicating that they can be applied to the field of optical storage materials. In this paper we also present a new insight into the photoinduced phase transition process of this material. The mechanism of photoinduced phase transition from λ-Ti₃O₅ to β-Ti₃O₅ is considered as stimulated emission effect. The results are of significance particularly for practically applying Ti₃O₅ and understanding its phase change mechanism.