In optoelectronic device applications, perovskite materials have overtaken other compounds because of their exceptional power conversion efficiencies. Lead-based perovskites have found extensive use; however, their widespread adoption is hindered by the inherent toxicity associated with lead content. In contrast, lead-free metal halide perovskites have taken the dominant position in the commercialization of optoelectronic devices by offering high efficiency, affordability, flexibility, tunability, and environmental benefits. To better understand the structural, electronic, bonding, optical, elastic, and mechanical properties of the non-toxic MSnI3 (M = K, Rb) metal halides under different hydrostatic pressures, a first-principles simulation has been carried out with the use of density functional theory (DFT). Lattice parameters and electronic band structures have been computed using both the Generalized Gradient Approximation (GGA) and the non-local hybrid sX (Hartree-Fock screened exchange) functional. Utilizing the sX method results in enhanced band gap values for MSnI3 (M = K, Rb) perovskite compounds. The application of pressure has led to a decrease in both lattice parameters and band gaps, marking a transition from a semiconductor to a metallic state. The projection of the density of states and their electronic orbital contributions are also explored to evaluate the band structure tuning of MSnI3 (M = K, Rb) under pressure. The bond length calculation and the charge density mapping confirm the existence of both the ionic and covalent bonds in MSnI3 (M = K, Rb). Additionally, the pressure-induced calculation suggests that the bonds between both compounds will be stronger at high pressure. Increasing hydrostatic pressure causes a dramatic movement of the absorption edge of MSnI3 (M = K, Rb) perovskites into the low energy region (a red shift), which is revealed by the analysis of optical functions. The optical functions’ investigation indicates that the hydrostatic pressure allows the compounds even better for a number of possible uses. The mechanical qualities are a direct reflection of the ductile and anisotropic nature of the compounds, both of which are significantly influenced by the external pressure.