Abstract Purpose To compare the effects of upper versus the lower-body resistance exercise on cognitive and physical functions of institutionalized older people. Methods This was a non-randomized multi-center comparative and crossover study (clincialtrials.gov code NCT03831373). Two experimental groups performed a 12-week intervention of resistance exercises with low-intensity elastic bands, one program focused on exercises of the upper body (n = 20, mean age 87.6 ± 6.4 years, 75% women) and the other on the lower body (n = 29, mean age 81.4 ± 7.7 years, 55% women). Following 12 weeks of detraining, the groups performed the other intervention. After another 12 weeks, a follow-up assessment was carried. The control group (n = 19, mean age 81.3 ± 9.5, 68% women) performed a full body stretching exercise program in both phases. Before and after each period, cognitive and physical function was assessed by standardized test (Mini-Mental State Examination, Trail Making test and Phototest; Timed Up and Go, Back Scratch, Chair Sit and Reach and had grip strength, respectively). Intention-to-treat and per-protocol analyses were carried. Results After the first intervention, significant improvements (p < 0.05) were observed in the cognitive function in both experimental groups, and in the hand grip strength in the group that performed lower-body exercise. After the second phase, all groups showed improvements in lower-body and shoulder flexibility and a significant worsening in hand grip strength. The lower-body exercise group showed a worsening in cognitive function, and the upper-body group in functional mobility and dynamic balance. Conclusions Resistance exercise with elastic bands showed beneficial effects on cognitive function and functional independence in institutionalized older adults. While upper body exercises seemed to be more effective on cognitive function, lower limb exercises showed better results on physical function parameters.