Cavitation is a phenomenon that occurs when the internal pressure of a material exceeds the resistance to deformation provided by the surrounding medium. Several measurements, such as the blister test, bubble inflation, and cavitation rheology, take advantage of this phenomenon to measure the local mechanical properties of soft materials at relatively low deformation rates. Here, we introduce a new measurement called laser-induced membrane expansion (LIME) that measures the shear modulus of a thin membrane at high strain rates (≈10⁶ s⁻¹ to 10⁸ s⁻¹) by using laser ablation to rapidly expand a thin (tens of microns) elastomeric membrane. To demonstrate the capabilities of this measurement, we use LIME to study the mechanical properties of poly(dimethylsiloxane) (PDMS) membranes at several thicknesses (from 10 μm to 60 μm) and crosslink densities. We find that the shear modulus of the PDMS measured by LIME was weakly dependent on the crosslink density, but was strongly strain rate dependent with values ranging from 10⁶ Pa to 10⁸ Pa. This measurement platform presents a new approach to studying the mechanical properties of soft but thin materials over a range of deformation rates.