The effect of the dimensions of the thoracic cage on the resuscitation outcome of cardiopulmonary resuscitation (CPR) maneuvers has long been debated. In this study, the effect of changes in the rib cage dimensions on the achieved compression depth was investigated using finite element simulations. A total of 216 different rib cage geometry models were considered and, in each case, the result of applying different levels of compression force up to 600 N were simulated. The Haller Index of the rib cage is defined as the ratio of the transverse diameter and the antero-posterior diameter. Our results suggest that, with a fixed level of compression force, performing CPR on rib cages having a low Haller Index and/or a larger height leads to compression depths below the average. Alternatively, if a target compression depth is set for CPR, in general a lower compression force would be required for individuals with higher Haller Index and/or lower chest height. In addition, present results indicate that wider chested individuals will experience lower stress levels on their ribs to achieve the required CPR target depth. Moreover, in the present study we propose predictive models, based on anthropometric parameters, for compression depth and rib stress during chest compressions. In particular, the model suggests that in future correlations of empirical CPR data the patients' Haller index and vertical (sagittal) cross-area are the best parameters to be used as independent variables in a fit.