<p>We perform a first-principles high-throughput screening of the mechanical properties of phonon-mediated superconductors derived from the recent experimentally synthesized superconducting materials database <a href="https://journals.aps.org/prxenergy/abstract/10.1103/sb28-fjc9">PRX Energy \textbf{4}, 033012 (2025)</a>. We develop the <a href="https://github.com/aiidaplugins/aiida-mechanical" target="_blank" rel="noopener">aiida-mechanical workflow</a> which combines first-principles calculations of elastic constants and generalized stacking fault energies, to assess the ductility of superconducting candidates. Starting from 250 materials identified with promising superconducting critical temperatures, we computed their elastic tensors to evaluate the bulk modulus, shear modulus, Pugh's ratio, and Pettifor's ratio. To further characterize their plastic deformation behavior, we calculated the stacking fault energy and surface energy for selected materials and slip directions, allowing the estimation of Rice's ratio and related ductility indicators. We find that several new materials simultaneously exhibit high T<sub>c</sub> and ductility, including HfPd<sub>2</sub>Al, TiRuSb, and ZrNi<sub>2</sub>Ga. This dataset provides the complete computational provenance. Specifically, it contains the fully relaxed crystal structures, Quantum ESPRESSO calculations for all elastic tensor (finite-displacement and Born approximation methodologies) and stacking fault energy workflows, as well as k-point and supercell convergence tests. This work offers a quantitative mapping of mechanical performance across a wide range of superconductors and provides a valuable reference for finding new practical superconducting materials.</p>