This study investigates the ASc2S4 (A = Ca, Sr) compounds having an AB2O4-type structure of orthorhombic crystal nature. The calculated formation enthalpies reveal the thermodynamic stability of these compounds. In addition, the mechanical and dynamical stabilities are found as well. The detailed electronic properties are studied using Perdew-Burke-Ernzerhof functional within the Generalized Gradient Approximation (GGA-PBE) and DFT + U methods. The ASc2S4 compounds are found to be semiconductor due the electronic band structures. The band gaps are determined as 1.11 eV and 1.25 eV using the GGA-PBE method, and 1.54 eV and 1.64 eV using the DFT + U method for CaSc2S4 and SrSc2S4, respectively. The orbital contributions to the partial density of states are investigated in detail. Furthermore, the optical properties of these compounds are obtained using the Bethe-Salpeter Equation (BSE) to consider the electron-hole interactions. The optical properties of the ASc2S4 compounds such as refractive indexes, extinction coefficients, absorption coefficients and loss functions are determined. This study fills the gap in the literature concerning the compounds that have S atoms instead of O atoms in AB2O4, while also revealing the electronic and optical properties of ASc2S4 (A = Ca, Sr) compounds in detail.