Continuum-scale modeling techniques are frequently used to simulate the elasto-plastic deformation of rechargeable battery's electrode materials during intercalation. The primary objective of this paper is to explore and compare the mathematical formulations, the ease of implementations and parametrization of two such techniques that are extensively used to represent the physics of ions intercalation in rechargeable battery electrodes. The first technique is a finite element coupled diffusion/structure mechanics (CDSM) model, and the second is a phase-field model (PFM). In the present work, the two models are compared quantitatively utilizing an example based upon lithiation of silicon. It is observed that the two models provide essentially similar results; however, their implementations and parameters clarification are significantly diverse. The detailed discussion in the paper identifies the merits and limitations of each model in the context of the assumptions in their theoretical formulations and their influence on the physics of diffusion/intercalation and deformation. Hence, the paper delivers new insights regarding the ranges of applicability and helps to understand similarities and differences between the two models. (c) 2017 The Electrochemical Society. All rights reserved.