The experimental quantification and modeling of the multiaxial mechanical response of polymer membranes of coronary balloon catheters have not yet been carried out. Due to the lack of insights, it is not shown whether isotropic material models can describe the material response of balloon catheter membranes expanded with nominal or higher, supra-nominal pressures. Therefore, for the first time, specimens of commercial polyamide-12 balloon catheters membranes were investigated during uniaxial and biaxial loading scenarios. Furthermore, the influence of kinematic effects on the material response was observed by comparing results from quasi-static and dynamic biaxial extension tests. Novel clamping techniques are described, which allow to test even tiny specimens taken from the balloon membranes. The results of this study reveal the semi-compliant, nonlinear, and viscoelastic character of polyamide-12 balloon catheter membranes. Above nominal pressure, the membranes show a pronounced anisotropic mechanical behavior with a stiffer response in the circumferential direction. The anisotropic feature intensifies with an increasing strain-rate. A modified polynomial model was applied to represent the realistic mechanical response of the balloon catheter membranes during dynamic biaxial extension tests. This study also includes a compact set of constitutive model parameters for the use of the proposed model in future finite element analyses to perform more accurate simulations of expanding balloon catheters.