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Optoelectronic functional materials with flexible and in-plane anisotropic properties has been a significant development direction of nanotechnology due to wearable and polarized optoelectronic applications. Herein, the elasticity, global band dispersion, optical dielectric properties of environmentally friendly IVB-VIA layered transition metal trichalcogenides (MX3, M = Zr, Hf; X = S, Se) are investigated systematically by density functional theory with different kinds of van der Waals correction and hybrid functional. The low elastic modulus suggests that they are appropriate for the design of flexible optoelectronic devices. Originating from the effect of d states of chalcogens and s states of transition metals, the dispersion of the valence band edge of monolayer MX3 shows that the effective mass of carriers along the wave vector kx is much heavier than that of carriers along the wave vector ky. This means that the mobility of carriers exhibits obvious in-plane anisotropy. Meanwhile, the optical dielectric properties of monolayer MX3 as well as absorbed photon flux (Jabs) of the related heterostructures display noteworthy in-plane anisotropy in the visible-IR region. The ratio of Jabs from different direction reaches up to 1.7. This work could not only promote understanding of rich photophyiscal properties of transition metal trichalcogenides, but also provide a theoretical reference for the invention of high-performance optoelectronic devices with high flexibility and anisotropy. [ABSTRACT FROM AUTHOR]