Amorphous solid-state electrolytes are attractive candidates for safe, high-energy-density all-solid-state batteries, yet their mechanical properties remain poorly understood from a computational perspective. Here, we investigate the elastic behavior of the recently discovered amorphous superionic Li-ion conductor LiTaCl₆ using density-functional-theory (DFT)-based methods, including unrelaxed static, relaxed static, and strain fluctuations from molecular dynamics (MD) simulations in the isobaric–isothermal (NPT) ensemble with DFT-trained machine-learning force fields (MLFFs). While the unrelaxed static method predicts a Young's modulus an order of magnitude higher than the experiment, the relaxed static method—commonly applied to crystalline electrolytes—still overestimates the modulus by more than 170%. In contrast, the MD approach using MLFFs yields a Young's modulus of 2.84 ± 0.26 GPa, which quantitatively agrees with the experimental value of 2.91 ± 0.32 GPa. Using the MLFF-MD approach, we further predict bulk modulus (4.44 GPa), shear modulus (1.02 GPa), and Poisson's ratio (0.39) for amorphous LiTaCl₆ and conclude that elastically it behaves like a soft polymer or gel. These results demonstrate that amorphous superionic materials possess some unique elastic properties and that, among the methods examined, only the MLFF-MD approach yields quantitative agreement with experiment, highlighting the necessity of a dynamical treatment to simulate their elastic response, consistent with recent findings for crystalline superionic conductors.