Objectives: The aim of this article was to identify the best predictors of distress suffered by family carers (FCs) of geriatric patients. Methods: A cross-sectional study of 100 FC-geriatric patient dyads was conducted. The negative impact of care (NIoC) subscale of the COPE index was dichotomized to identify lower stress (score of #15 on the scale) and higher stress (score of ≤16 on the scale) exerted on FCs by the process of providing care. The set of explanatory variables comprised a wide range of sociodemographic and care-related attributes, including patient-related results from comprehensive geriatric assessments and disease profiles. The best combination of explanatory variables that provided the highest predictive power for distress among FCs in the multiple logistic regression (LR) model was determined according to statistical information criteria. The statistical robustness of the observed relationships and the discriminative power of the model were verified with the cross-validation method. Results: The mean age of FCs was 57.2 (±10.6) years, whereas that of geriatric patients was 81.7 (±6.4) years. Despite the broad initial set of potential explanatory variables, only five predictors were jointly selected for the best statistical model. A higher level of distress was independently predicted by lower self-evaluation of health; worse self-appraisal of coping well as a caregiver; lower sense of general support; more hours of care per week; and the motor retardation of the cared-for person measured with the speed of the Timed Up and Go (TUG) test. Conclusion: Worse performance on the TUG test was only the patient-related predictor of distress among the variables examined as contributors to the higher NIoC. Enhancing the mobility of geriatric patients through suitably tailored kinesitherapeutic methods during their hospital stay may mitigate the burden endured by FCs.