Solid polymer electrolyte (SPE) membranes are a critical component of high specific energy rechargeable Li-metal polymer (LMP) batteries. SPEs exhibit low volatility and thus increase the safety of Li-based batteries compared to current state-of-the-art Li-ion batteries that use flammable small-molecule electrolytes. However, most SPEs exhibit low ionic conductivity at room temperature, and often allow the growth of lithium dendrites that short-circuit the batteries. Both of these deficiencies are significant barriers to the commercialization of LMP batteries. Herein we report a cross-linked polyethylene/poly(ethylene oxide) SPE with both high ionic conductivity (>1.0 × 10(-4) S/cm at 25 °C) and excellent resistance to dendrite growth. It has been proposed that SPEs with shear moduli of the same order of magnitude as lithium could be used to suppress dendrite growth, leading to increased lifetime and safety for LMP batteries. In contrast to the theoretical predictions, the low-modulus (G' ≈ 1.0 × 10(5) Pa at 90 °C) cross-linked SPEs reported herein exhibit remarkable dendrite growth resistance. These results suggest that a high-modulus SPE is not a requirement for the control of dendrite proliferation.