Empirically derived sensitivities of streamflow to precipitation are often assumed to be temporally unchanging. This assumption may be unrealistic because changes in climate and storage are known to alter this relationship. We present a non-stationary regional regression approach which is functionally similar to typical elasticity estimation approaches. This is applied to 2967 catchments in the United States to estimate variability in interannual, and trends in long-term, streamflow elasticity to precipitation over a 39-year period. We show that interannual elasticity is highly variable in water-limited catchments, indicating that these are especially sensitive to year-to-year climate variability, as compared to other regions. Interannual elasticity is more often correlated with the one-year lagged standardized precipitation index than with temperature or in-phase standardized precipitation index, suggesting that antecedent soil moisture, groundwater storage, and precipitation seasonality influence streamflow sensitivity. Finally, statistically significant long-term trends in elasticity exist in some regions, but trend magnitude is generally small. These findings suggest that an assumption of stationarity in long-term average elasticity may still be appropriate at the regional scale, however, year-to-year variation in streamflow responsiveness to precipitation is often substantial.