Catheter surgery is a minimally invasive treatment in which visual information is limited to a two-dimensional image generated by an X-ray camera. This results in the possibility that stress applied by the catheter onto a blood vessel wall damages the vessel. Doctors must therefore be skillful at catheter surgery. We proposed a catheter surgery simulator that visualizes the stress applied to the blood vessel wall using photoelasticity. The manufacture of this simulator requires creating blood vessel mimics that reproduce the physical properties of blood vessel tissue using photoelasticity. This study investigated the mechanical and photoelastic properties of gel materials and selected a gel composition suitable for making blood vessel mimics. The mechanical properties of polyvinyl alcohol (PVA) hydrogel changed in the range 70–335 kPa by changing the composition ratio, and double network (DN) gel changed in the range 0.13–1.06 MPa by changing the composition ratio. These gels could be adjusted by changing the material composition to provide Young's moduli similar to that of blood vessels. The photoelastic properties of PVA hydrogel changed in the range 1.38–2.76 × 10−9/Pa by changing the composition ratio, and DN gel changed in the range 0.012–0.029 × 10−9/Pa by changing the composition ratio.