We present strong gravitational lensing models for 37 galaxy clusters from the Sloan Digital Sky Survey Giant Arcs Survey (SGAS). We combine data from multi-band Hubble Space Telescope Wide Field Camera 3 (WFC3) imaging, with ground-based imaging and spectroscopy from Magellan, Gemini, Apache Point Observatory, and the Multiple Mirror Telescope, in order to detect and spectroscopically confirm new multiply imaged lensed background sources behind the clusters. We report spectroscopic or photometric redshifts of sources in these fields, including cluster galaxies and background sources. Based on all available lensing evidence, we construct and present strong-lensing mass models for these galaxy clusters. The clusters span a redshift range of 0.176<z<0.66 with a median redshift of z=0.45, and sample a wide range of dynamical masses, 1.5<M_200_<35x10^14^M_{sun}_, as estimated from their velocity dispersions. As these clusters were selected as lenses primarily owing to a fortuitous alignment with background galaxies that results in giant arcs, they exhibit a wide range in Einstein radii, 1.3"<{theta}_E_<23.1" for a source at z=2, with a median {theta}_E_=10.8".