Since the 1970s, part of the solid rocket motor (SRM) has experienced disintegration when the tactical missile is launched at a low temperature of −40 °C. Analyses of the emission of a large number of solid missiles revealed that the destruction of the structural integrity of the solid propellant grain was the major contributor to SRM failure. Due to the coupled effects of low temperature and the ignition pressure load, the structure integrity of solid propellant grain is aggravated. Therefore, improving the structure integrity of propellant grain during the ignition of SRM for tactical missiles at low temperatures is one of the key problems to tackle during the research and production of weapons. As previous reports show, the mechanical behaviors of solid propellants at low temperatures and strain rates from 1 to 102 s−1 are very important to effectively analyze the structure integrity of propellant grain for SRM of the tactical missiles during ignition at low temperatures. However, the mechanical behaviors of thermal aging solid propellants at low temperatures under dynamic loading are rarely reported. It is urgent to carry out research in this regard through new mechanical test methods. In this paper, we analyze the research progress of biaxial tensile testing schemes for different materials such as metals and composite materials. It was found that there are currently many biaxial tensile tests on rubber and composite materials, which can provide effective references for other materials.