This work presents an application of the strain-fluctuation method, exploiting the fluctuations of the strain from extensive first-principles molecular dynamics simulations in the isobaric-isothermal ensemble, to the study of the elastic tensors of superionic materials. As the superionic materials for solid-state electrolyte applications usually do not have well-defined ground-state configurations, it is challenging to apply the static methods to calculate the elastic tensors of these materials. Instead, the strain-fluctuation method captures the dynamical nature of the elastic response of these materials and is a promising approach to studying their elastic properties. In this work: a protocol is presented and documented to extract the elastic the elastic moduli and their statistical errors from the molecular dynamics trajectories (open-source code available at https://github.com/materzanini); results for two benchmark superionic materials (Li₁₀GeP₂S₁₂ and Li₁₀GeP₂O₁₂) are given; for these superionic materials, a comparison to static methods is also provided, showing that static methods overestimate the moduli with respect to the correct dynamical treatment by ~25-50%.