Using PP-APW method the electronic, optical and mechanical anisotropy of ZnRE2S4 (RE = Er, Tm) olivine compounds was investigated. The calculated unit cell parameters are in good agreement compared to the experimental ones. In addition, the study of electronic properties reveals that ZnEr2S4 and ZnTm2S4 are semiconductors with a direct bandgap of about 2.37 eV and 2.35 eV, respectively. The optical constants such as refractive index, reflectivity, and absorption coefficient have been calculated and analyzed. These constants show a clear anisotropy in the UV region for both compounds caused by the different electron polarizability in x-, y- and z-direction. Moreover, the elastic constants are estimated for the first time for ZnEr2S4 and ZnTm2S4 indicating that the compounds are mechanically stable and reveal ductility behavior. The direct bandgap, optical absorption, and mechanical stability make ZnEr2S4 and ZnTm2S4 promising candidates for optoelectronic application.