A key step in drug combination analysis is the selection of an additivity model to identify combination effects including synergy, additivity and antagonism. Existing methods for identifying and interpreting those combination effects have limitations. We present here a computational framework, termed response envelope analysis (REA), that makes use of 3D response surfaces formed by generalized Loewe Additivity and Bliss Independence models of interaction to evaluate drug combination effects. Because the two models imply two extreme limits of drug interaction (mutually exclusive and mutually non-exclusive), a response envelope defined by them provides a quantitatively stringent additivity model for identifying combination effects without knowing the inhibition mechanism. As a demonstration, we apply REA to representative published data from large screens of anticancer and antibiotic combinations. We show that REA is more accurate than existing methods and provides more consistent results in the context of cross-experiment evaluation.