Solid-state batteries offer an alternative promising power source for electric vehicles. However, the interfacial mechanical stability of inorganic electrolytes is inferior to that of organic electrolytes. A high stack pressure (several to hundreds of megapascals) is often required to maintain intimate contact with electrodes. Here we report a class of viscoelastic inorganic glass (VIGLAS) to serve as solid electrolytes by simply replacing chlorine of tetrachloroaluminates with oxygen. The VIGLAS possesses high ionic conductivity (~1 mS cm⁻¹ at 30 °C) for both Li⁺ and Na⁺, superior chemo-mechanical compatibility with 4.3 V cathodes and the ability to enable pressure-less Li- and Na-based solid-state batteries (<0.1 MPa). The low melting temperature (<160 °C) allows the electrolytes to efficiently infiltrate electrode materials, akin to a liquid battery. Additionally, the deformability of the electrolytes facilitates the feasibility of scale-up through the production of thin films via a rolling process.